GENERALIZED RIEMANNIAN GEOMETRY, II

Generalized pseudo-Riemannian geometry

Generalized tensor analysis in the sense of Colombeau’s construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of generalized functions we define the notions of generalized pseudo-Riemannian metric, generalized connection and generalized curvature tensor. We prove a “Fun...

The Einstein Generalized Riemannian Geometry.

s, p. 85. 2 Eggers, H. J., Cold Spring Harbor Symposia on Quantitative Biology, vol. 27 (1962) 309. 3Loddo, B., W. Ferrari, A. Spanedda, and G. Brotzu, Experientia, 18, 518 (1962). 4Ledinko, N., Cold Spring Harbor Symposia on Quantitative Biology, vol. 27 (1962) 309. 5 Eggers, H. J., and I. Tamm, J. Exptl. Med., 113, 657 (1961). 6 Eggers, H. J., and I. Tamm, Virology, 13, 545 (1961). 7Rightsel,...

A Geometry Preserving Kernel over Riemannian Manifolds

Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...

Generalized Cylinders in Semi-riemannian and Spin Geometry

We use a construction which we call generalized cylinders to give a new proof of the fundamental theorem of hypersurface theory. It has the advantage of being very simple and the result directly extends to semi-Riemannian manifolds and to embeddings into spaces of constant curvature. We also give a new way to identify spinors for different metrics and to derive the variation formula for the Dir...

Riemannian geometry