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Ημι-ομοιόμορφοι και Lqu - χώροι: ημι-μετρικοποιησιμότητα διάταξη και συμπλήρωσηΑνδρικόπουλος, Αθανάσιος 30 September 2009 (has links)
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Projective structure on 4-dimensional manifoldsWang, Zhixiang January 2012 (has links)
The object of my thesis is to investigate projectively related metrics, that is, metrics whose Levi-Civita connections admit exactly the same family of unparametrised geodesics on 4-dimensional manifolds with positive de nite or neutral (+;+;;) signatures. The general idea is to study the relationship between projectively related metrics and the holonomy types of each metric. The main technique presented in the work requires a certain classification of the curvature map which has been developed by G. S. Hall and D. P. Lonie in the case of Lorentz signature. In chapter 1, some of the background theory will be given. This will include an introduction to bivector algebra, a revision of the Riemann curvature tensor and holonomy theory and, in particular, the fundamental equations for projective related metrics. A brief historical and bibliographical review is also given. The subsequent chapter gives the details of projective related metrics of positive definite signature. In x2.1, the structure of so(4) is described with an emphasis on the canonical decomposition of bivectors and then the subalgebras of so(4) follow. In x2.2., the problem of projective related metrics can be solved case by case decided by holonomy types. In many of these cases, the connections are found to be necessarily equal. A few cases with nontrivial projectively related metrics have been found by only in the rather special case of curvature class D, and the metrics are given in the appendices. An extension of this method to spaces of neutral signature (+;+;;) is made in chapter 3. The rst part of the chapter discusses the algebraic structure of a 4-dimensional vector space with such a metric. In contrast to metrics of the other two signatures (positive definite and Lorentz), this metric admits totally null planes. The structure of the Lie algebra so(2; 2) can be described through the action on totally null planes. The classification of all subalgebras of so(2,2) is then obtained in terms of self-dual and anti-self-dual bivectors. In most holonomy types and curvature classes, the problem has only trivial solutions. Nontrivial projectively related metrics can be found for four holonomy types with curvature class D and two holonomy types with curvature class A.
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Advanced compulsator topologies and technologiesWalls, William Alan 09 May 2011 (has links)
Not available / text
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Ultrafilters and topologies黃毅英, Wong, Ngai-ying. January 1981 (has links)
published_or_final_version / Mathematics / Master / Master of Philosophy
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PROBABILISTIC METRICS AND PROBABILITY MEASURES ON METRICSStevens, Robert Ray, 1935- January 1965 (has links)
No description available.
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PRODUCTS AND QUOTIENTS OF PROBABILISTIC METRIC SPACESEgbert, Russell James, 1937- January 1966 (has links)
No description available.
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TOPOLOGY OF TORUS-LIKE FIBER SPACESHall, Michael Henry, 1939- January 1966 (has links)
No description available.
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Compactness and related conceptsKneece, Roland Royce 08 1900 (has links)
No description available.
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Convergences and topologies for families of functionsBrown, David Lyle 08 1900 (has links)
No description available.
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An investigation of ultrametric spacesElkins, Benjamin Joseph 12 1900 (has links)
No description available.
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