I construct anti-de Sitter boson stars in Einstein-Gauss-Bonnet gravity coupled to a (D-1)/(2)-tuplet of complex massless scalar field both perturbativelyand numerically in D=5,7,9,11 dimensions. Due to the choice of scalar fields, these solutions possess just a single helical Killing symmetry. For each choice of the Gauss-Bonnet parameter &alpha;&#8800;&alpha;_cr, the central energy density at the center of the boson star, q_0 completely characterizes the one parameter family of solutions. These solutions obey the first law of thermodynamics, in the case of the numerics, to within 1 part in 10^6. I describe the dependence of the boson star mass, angular momentum and angular velocity on &alpha; and on the dimensionality. For &alpha;<&alpha;_cr and D>5, these quantities exhibit damped oscillations about finite central values and the central energy density tends to infinity. The Kretschmann invariant at the center of the boson star diverges in the limit of diverging central energy. This contrasts the D=5 case, where the Kretschmann invariant diverges at a finite value of the central energy density. Solutions where &alpha;<&alpha;_cr, correspond to negative mass boson stars, and the for all dimensions the boson star mass and angular momentum decrease exponentially as the central energy density tends toward infinity with the Kretschmann invariant diverging only when in the limit the central energy density diverges. I also briefly discuss the difficulties of numerically obtaining single Killing vector hairy black hole solutions and present the explicit boundary conditions for both Einstein gravity and Einstein-Gauss-Bonnet gravity.

Phytophthora infestans (Mont) de Bary is a devastating pathogen in potato producing regions around the world. Populations of the organism in Canada shifted during the mid-1990’s as the US-1 strain (A1, metalaxyl-sensitive) was displaced by the highly aggressive, US-8 strain (A2, metalaxyl-insensitive). An increase in the incidence and severity of late blight has followed. Late blight is controlled by cultural practices aimed at eliminating disease sources and by the application of foliar fungicides. Tubers can become infected at harvest from contact with blighted vines leading to severe losses in storage. In many production areas, growers desiccate vines two to three weeks prior to harvest to reduce late blight tuber rot. However, in Manitoba, because of the loss of potential yield that results from vine killing prior to harvest in a late maturing cultivar such as Russet Burbank, growers are reluctant to adopt this practice. The objective of this study was to develop recommendations for preharvest management practices that reduce storage losses due to late blight. Field trials were conducted in 1997 and 1998 to investigate the effect of vine desiccation with diquat and/or a late season application of chlorothalonil and copper hydroxide on yield, processing quality, and disease development in storage. Desiccating vines with diquat two weeks prior to harvest reduced yield and tuber size. Compared to the untreated control, the largest reductions in marketable yield were observed for the early September harvest. By the late September harvest, however, the effect of vine killing in reducing marketable yield was less apparent. Specific gravity was lower in the vine killed treatment for all harvest dates in 1997 and in the early and mid September harvests in 1998. Vine killing did not contribute to elevated levels of reducing sugars or consistently darker fry colour at harvest or during storage. Skin-set was improved when vines were desiccated for all harvest dates in 1997 and at the early September harvest date in 1998. Vine killing reduced tuber rot in storage caused by Fusarium dry rot and Pythium leak for the early and mid September harvest dates in 1997. The incidence of late blight tuber rot was reduced in storage for the early September harvest in 1998 when vines were desiccated. The late-season application of chlorothalonil and copper hydroxide did not reduce tuber rot in storage in storage either year. Results from this study indicate that vine killing two weeks before an early to mid- September harvest is not recommended in Manitoba because of reductions in yield and specific gravity. Alternative management practices to reduce late blight tuber rot in storage should be investigated.

Phytophthora infestans (Mont) de Bary is a devastating pathogen in potato producing regions around the world. Populations of the organism in Canada shifted during the mid-1990’s as the US-1 strain (A1, metalaxyl-sensitive) was displaced by the highly aggressive, US-8 strain (A2, metalaxyl-insensitive). An increase in the incidence and severity of late blight has followed. Late blight is controlled by cultural practices aimed at eliminating disease sources and by the application of foliar fungicides. Tubers can become infected at harvest from contact with blighted vines leading to severe losses in storage. In many production areas, growers desiccate vines two to three weeks prior to harvest to reduce late blight tuber rot. However, in Manitoba, because of the loss of potential yield that results from vine killing prior to harvest in a late maturing cultivar such as Russet Burbank, growers are reluctant to adopt this practice. The objective of this study was to develop recommendations for preharvest management practices that reduce storage losses due to late blight. Field trials were conducted in 1997 and 1998 to investigate the effect of vine desiccation with diquat and/or a late season application of chlorothalonil and copper hydroxide on yield, processing quality, and disease development in storage. Desiccating vines with diquat two weeks prior to harvest reduced yield and tuber size. Compared to the untreated control, the largest reductions in marketable yield were observed for the early September harvest. By the late September harvest, however, the effect of vine killing in reducing marketable yield was less apparent. Specific gravity was lower in the vine killed treatment for all harvest dates in 1997 and in the early and mid September harvests in 1998. Vine killing did not contribute to elevated levels of reducing sugars or consistently darker fry colour at harvest or during storage. Skin-set was improved when vines were desiccated for all harvest dates in 1997 and at the early September harvest date in 1998. Vine killing reduced tuber rot in storage caused by Fusarium dry rot and Pythium leak for the early and mid September harvest dates in 1997. The incidence of late blight tuber rot was reduced in storage for the early September harvest in 1998 when vines were desiccated. The late-season application of chlorothalonil and copper hydroxide did not reduce tuber rot in storage in storage either year. Results from this study indicate that vine killing two weeks before an early to mid- September harvest is not recommended in Manitoba because of reductions in yield and specific gravity. Alternative management practices to reduce late blight tuber rot in storage should be investigated.

On the tangent bundle of a Riemannian manifold the most natural choice of metric tensor field is the Sasaki metric. This immediately brings up the question of infinitesimal symmetries associated with the inherent geometry of the tangent bundle arising from the Sasaki metric. The elucidation of the form and the classification of the Killing vector fields have already been effected by the Japanese school of Riemannian geometry in the sixties. In this thesis we shall take up the conformal vector fields of the Sasaki metric with the help of relatively advanced techniques.

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Um resultado clássico em Geometria Diferencial, conhecido como teorema de Hadamard, e demonstrado pelo mesmo ([Ha]), estabelece que uma superfície conexa compacta no espaço Euclidiano cujas curvaturas principais são todas positivas é o bordo de um corpo convexo. Em part icular, a superfície é difeomorfa a uma esfera. Neste trabalho apresentamos extensões parciais deste teorema para imersões de codimensão arbitrária e para outros espaços ambientes que o E uclidiano conforme feito em [R]. / A classical result in differential geometry, known as Hadamard's theorem and proved by himself ([Ha]). establishes that a compact connected surface in the Euclidean space whose principal curvatures are everywhere positive is the boundary of a convex body. In particular, the surface is diffeomorphic to a sphere. In this work we present IJartial extensions of this theorem to immersions of arbitrary codimension and to other spaces than the Euclidean one, as clone in [R].

Neste trabalho mostramos que dado um domínio exterior de classe C0 contido em uma superfície umb lica de H3; com curvatura média constante H 2 [0; 1); existe uma família de gracos de Killing com curvatura média constante H: O bordo de cada um destes gracos está contido nesta superfície umbílica e a norma do gradiente da função no bordo pode ser prescrita por um certo valor s 0. / In this paper we show that given an exterior domain of class C0 contained in an umbilical surface of H3; with constant mean curvature H 2 [0; 1); there exists a family of Killing graphs with constant mean curvature H: The boundary of each of these graphs is contained in this umbilical surface and the norm of the gradient of the function in the boundary can be prescribed by a certain value s 0:

Neste trabalho mostramos que dado um domínio exterior de classe C0 contido em uma superfície umb lica de H3; com curvatura média constante H 2 [0; 1); existe uma família de gracos de Killing com curvatura média constante H: O bordo de cada um destes gracos está contido nesta superfície umbílica e a norma do gradiente da função no bordo pode ser prescrita por um certo valor s 0. / In this paper we show that given an exterior domain of class C0 contained in an umbilical surface of H3; with constant mean curvature H 2 [0; 1); there exists a family of Killing graphs with constant mean curvature H: The boundary of each of these graphs is contained in this umbilical surface and the norm of the gradient of the function in the boundary can be prescribed by a certain value s 0:

Um resultado clássico em Geometria Diferencial, conhecido como teorema de Hadamard, e demonstrado pelo mesmo ([Ha]), estabelece que uma superfície conexa compacta no espaço Euclidiano cujas curvaturas principais são todas positivas é o bordo de um corpo convexo. Em part icular, a superfície é difeomorfa a uma esfera. Neste trabalho apresentamos extensões parciais deste teorema para imersões de codimensão arbitrária e para outros espaços ambientes que o E uclidiano conforme feito em [R]. / A classical result in differential geometry, known as Hadamard's theorem and proved by himself ([Ha]). establishes that a compact connected surface in the Euclidean space whose principal curvatures are everywhere positive is the boundary of a convex body. In particular, the surface is diffeomorphic to a sphere. In this work we present IJartial extensions of this theorem to immersions of arbitrary codimension and to other spaces than the Euclidean one, as clone in [R].