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11 
Harmonic maps in Kähler geometry盧貴榮, Lo, Kwaiwing, Eric. January 1997 (has links)
published_or_final_version / Mathematics / Master / Master of Philosophy

12 
Twist or theory of immersions of surfaces in fourdimensional spheres and hyperbolic spacesFawley, Helen Linda January 1997 (has links)
Let f : S → S(^4) be an immersion of a Riemann surface in the 4sphere. The thesis begins with a study of the adapted moving frame of / in order to produce conditions for certain naturally defined lifts to SO(5)/U(2) and S0(5)T(^2) to be conformal, harmonic and holomorphic with respect to two different but naturally occuring almost complex structures. This approach brings together the results of a number of authors regarding lifts of conformal, minimal immersions including the link with solutions of the Toda equations. Moreover it is shown that parallel mean curvature immersions have hajmonic lifts into S0(5)/U(2).A certain natural lift of / into CP(^3), the twistor space of S(^4), is studied more carefully via an explicit description and in the case of / being a conformal immersion this gives a beautiful and simple formula for the lift in terms of a stereographic coordinate associated to /. This involves establishing explicitly the twotoone correspondence between elements of the matrix groups Sp(2) and SO(5) and working with quaternions. The formula enables properties of such lifts to be explored and in particular it is shown that the harmonic sequence of a harmonic lift is either finite or satisfies a certain symmetry property. Uniqueness properties of harmonic lifts are also proved. Finally, the ideas are extended to the hyperbolic space H(^4) and after an exposition of the twistor fibration for this case, a method for constructing superminimal immersions of surfaces into H'^ from those in S"' is given.

13 
Constructions of harmonic maps between Hadamard manifolds /Ueno, Keisuke. January 2001 (has links)
Univ., Diss.Sendai.

14 
Harmonic maps in Kähler geometry /Lo, Kwaiwing, Eric. January 1997 (has links)
Thesis (M. Phil.)University of Hong Kong, 1997. / Includes bibliographical references (leaf 6166).

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Harmonic maps into trees and graphs analytical and numerical aspects /Hesse, Martin, January 2005 (has links)
Thesis (doctoral)Rheinische FriedrichWilhelmsUniversität Bonn, 2004. / Includes bibliographical references (p. 98100).

16 
The higher flows of harmonic mapsGagliardo, Michael Sebastian, January 1900 (has links)
Thesis (Ph. D.)University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

17 
Group invariant solutions for the system of harmonic map equations.January 2004 (has links)
Hung Ling Yan Lincoln. / Thesis (M.Phil.)Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 8788). / Abstracts in English and Chinese. / Chapter 1  Introduction  p.5 / Chapter 2  Preliminary  p.10 / Chapter 2.1  Background in geometry  p.10 / Chapter 2.2  Background in harmonic maps  p.12 / Chapter 3  Lie Point Transformations and Symmetries  p.16 / Chapter 3.1  Definition of symmetries  p.16 / Chapter 3.2  Determine the Lie point symmetries of partial differential equations  p.25 / Chapter 3.2.1  Second order differential equations  p.26 / Chapter 4  Similarity Variables  p.30 / Chapter 4.1  "Similarity variables and groupinvariant, solutions"  p.30 / Chapter 4.2  Reduction of number of variables of the partial differential equations  p.34 / Chapter 4.2.1  Determine the similarity variables  p.34 / Chapter 4.2.2  Procedure to reduce the number of variables of a system of partial differential equations  p.36 / Chapter 5  Group Invariant Harmonic Maps  p.38 / Chapter 5.1  Determine the Lie point symmetries of the harmonic map equations  p.39 / Chapter 5.2  Reduction of harmonic map equations to ordinary differ ential equations  p.54 / Chapter 5.3  Solving the harmonic map system which has been reduced to ordinary differential equations  p.62 / Chapter 5.3.1  Case 1 of Theorem 5.2.1  p.62 / Chapter 5.3.2  Case 2 of Theorem 5.2.1  p.66 / Chapter 5.3.3  Case 3 of Theorem 5.2.1  p.75 / Bibliography  p.87

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Singular harmonic maps into hyperbolic spaces and applications to general relativityNguyen, Luc L. January 2009 (has links)
Thesis (Ph. D.)Rutgers University, 2009. / "Graduate Program in Mathematics." Includes bibliographical references (p. 5152).

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Applications of harmonic mappings to rigidity problems /Chan, Yatming, January 2002 (has links)
Thesis (M. Phil.)University of Hong Kong, 2002. / Includes bibliographical references (leaves 112116).

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Applications of harmonic mappings to rigidity problemsChan, Yatming, 陳一鳴 January 2002 (has links)
published_or_final_version / Mathematics / Master / Master of Philosophy

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