Weighted Curvatures in Finsler Geometry

If you need an accessible version of this item, please email your request to digschol@iu.edu so that they may create one and provide it to you.
Date
2023-08
Language
American English
Embargo Lift Date
Department
Committee Chair
Degree
Ph.D.
Degree Year
2023
Department
Mathematical Sciences
Grantor
Purdue University
Journal Title
Journal ISSN
Volume Title
Found At
Abstract

The curvatures in Finsler geometry can be defined in similar ways as in Riemannian geometry. However, since there are fewer restrictions on the metrics, many geometric quantities arise in Finsler geometry which vanish in the Riemannian case. These quantities are generally known as non-Riemannian quantities and interact with the curvatures in controlling the global geometrical and topological properties of Finsler manifolds. In the present work, we study general weighted Ricci curvatures which combine the Ricci curvature and the S-curvature, and define a weighted flag curvature which combines the flag curvature and the T -curvature. We characterize Randers metrics of almost isotropic weighted Ricci curvatures and show the general weighted Ricci curvatures can be divided into three types. On the other hand, we show that a proper open forward complete Finsler manifold with positive weighted flag curvature is necessarily diffeomorphic to the Euclidean space, generalizing the Gromoll-Meyer theorem in Riemannian geometry.

Description
Indiana University-Purdue University Indianapolis (IUPUI)
item.page.description.tableofcontents
item.page.relation.haspart
Cite As
ISSN
Publisher
Series/Report
Sponsorship
Major
Extent
Identifier
Relation
Journal
Source
Alternative Title
Type
Thesis
Number
Volume
Conference Dates
Conference Host
Conference Location
Conference Name
Conference Panel
Conference Secretariat Location
Version
Full Text Available at
This item is under embargo {{howLong}}