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An index formula for simple graphs
Curvature topological invariants graph theory Euler characteristic
2012/5/24
Gauss-Bonnet for simple graphs G assures that the sum of curvatures K(x) over the vertex set V of G is the Euler characteristic X(G). Poincare-Hopf tells that for any injective function f on V the sum...
Index of quasi-conformally symmetric semi-Riemannian manifolds
Index of a semi-Riemannian manifold metric connection quasi-conformal curvature tensor
2012/2/29
We find the index of $\widetilde{\nabla}$-quasi-conformally symmetric and $\widetilde{\nabla}$-concircularly symmetric semi-Riemannian manifolds, where $\widetilde{\nabla}$ is metric connection.
K-homology and index theory on contact manifolds
K-homology and index theory Operator Algebras Differential Geometry
2011/8/31
Abstract: Let X be a closed connected contact manifold. On X there is a naturally arising class of hypoelliptic (but not elliptic) operators which are Fredholm. In this paper we solve the index proble...
A polyhedron in Euclidean 3-space is called a regular polyhedron of index 2 if it is combinatorially regular and its geometric symmetry group has index 2 in its combinatorial automorphism group; thus ...