Connections between Differential Geometry and Topology
نویسندگان
چکیده
منابع مشابه
Combinatorial Differential Topology and Geometry
A variety of questions in combinatorics lead one to the task of analyzing the topology of a simplicial complex, or a more general cell complex. However, there are few general techniques to aid in this investigation. On the other hand, the subjects of differential topology and geometry are devoted to precisely this sort of problem, except that the topological spaces in question are smooth manifo...
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The general setting here is that one would like to understand the classification of manifolds, and related objects such as knots in 3-space. The “classification”means up to an appropriate equivalence, and for definiteness we will consider smooth (i.e. differentiable) manifolds up to diffeomorphism (equivalence by differentiable homeomorphisms). Of course, what one really seeks is an understandi...
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We search for Riemannian metrics whose Levi-Civita connection belongs to a given projective class. Following Sinjukov and Mikeš, we show that such metrics correspond precisely to suitably positive solutions of a certain projectively invariant finite-type linear system of partial differential equations. Prolonging this system, we may reformulate these equations as defining covariant constant sec...
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Two types of properties for linear connections (natural and almost paracontact metric) are discussed in almost paracontact metric geometry with respect to four linear connections: Levi-Civita, canonical (Zamkovoy), Golab and generalized dual. Their relationship is also analyzed with a special view towards their curvature. The particular case of an almost paracosymplectic manifold giv...
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The architecture of Geographic Information Systems (GISs) is changing: more and more systems are based on the integrated architecture, i.e. storing geometric data in the Data Base Management System (DBMS) together with administrative data. The first step is having data types and operators for the simple features (i.e. geometric primitives): point, line and polygon. This has reached the level of...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1935
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.21.4.225