Riemannian geometry and geometric analysis

@inproceedings{Jost1995RiemannianGA,
  title={Riemannian geometry and geometric analysis},
  author={Jurgen Jost},
  year={1995}
}
* Established textbook * Continues to lead its readers to some of the hottest topics of contemporary mathematical research This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research.This new edition introduces and explains the ideas of the parabolic methods that have recently found such a spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discusses further examples… 
Aspects of Differential Geometry II
TLDR
The basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincare duality, and the Kunneth formula are proved, and a brief introduction to the theory of characteristic classes is given.
The Geometric Meaning of Curvature: Local and Nonlocal Aspects of Ricci Curvature
Curvature is a concept originally developed in differential and Riemannian geometry. There are various established notions of curvature, in particular sectional and Ricci curvature. An important
Explorations of Infinitesimal Inverse Spectral Geometry
Spectral geometry is a mathematical discipline that studies the relationship between the geometry of Riemannian manifolds and the spectra of natural differential operators defined on them. The
Index Theory with Applications to Mathematics and Physics
Index Theory with Applications to Mathematics and Physics describes, explains, and explores the Index Theorem of Atiyah and Singer, one of the truly great accomplishments of twentieth-century
The differential geometry of landmark shape manifolds: metrics, geodesics, and curvature
The study of shapes and their similarities is central in computer vision, in that it allows to recognize and classify objects from their representation. One has the interest of defining a distance
Applications of Affine and Weyl Geometry
TLDR
This book associates an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and uses this correspondence to study both geometries to be accessible to mathematicians who are not expert in the subject and to students with a basic grounding in differential geometry.
Preliminary Calculus on Manifolds
This chapter provides a preliminary knowledge of manifold. Manifold geometry is the foundation of the geometric approach to dimensionality reduction. In DR, we assume that the observed
On Perturbative Methods in Spectral Geometry
The goal of spectral geometry is to establish how much information about the geometry of compact Riemannian manifolds is contained in the spectra of natural differential operators, especially
Riemannian Geometry on Some Noncommutative Spaces
This dissertation enquires into how the theory and mechanism of Riemannian geometry can be introduced into and integrated with the existent ones in noncommutative geometry, a branch of mathematics
...
1
2
3
4
5
...