Kategoria BISAC: Mathematics >> Geometry - Non-Euclidean

The theory of D-modules deals with the algebraic aspects of differential equations. These are particularly interesting on homogeneous manifolds, since the infinitesimal action of a Lie algebra consists of differential operators. Hence, it is possible to attach geometric invariants, like the support and the characteristic variety, to representations of Lie groups. By considering D-modules on flag varieties, one obtains a simple classification of all irreducible admissible representations of reductive Lie groups. On the other hand, it is natural to study the representations realized by...

This graduate textbook begins by introducing Tensors and Riemannian Spaces, and then elaborates their application in solving second-order differential equations, and ends with introducing theory of relativity and de Sitter space. Based on 40 years of teaching experience, the author compiles a well-developed collection of examples and exercises to facilitate the reader s learning.

This text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called "arithmetic hyperbolic surfaces," the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in number theory to study them.

After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed...

Geometric Analysis is one of the most active research fields nowadays. The interplay between geometric and analytic techniques is at the core of recent remarkable advances in Differential Geometry and Topology. However, the majority of the monographs and books on the subject focus on intrinsic Riemannian Geometry techniques and applications. A systematic treatment of problems involving the extrinsic curvature of submanifolds is still missing in the literature. In particular, up to our knowledge, there are no references joining the geometric and analytic aspects of the theory of...