Curvature and Riemannian Submersions

Doctoral Dissertation

Abstract

We study Riemannian submersions from positively curved manifolds and from Einstein manifolds. We first prove a diameter rigidity theorem for Riemannian submersions.Secondly we show that there is no nontrivial Riemannian submersion from positively curved four manifolds such that either the mean curvature vector field or the norm of the O'Neill tensor is basic. We also classify Riemannian submersions from compact four-dimensional Einstein manifolds with totally geodesic fibers.

Attributes

Attribute NameValues
URN
  • etd-04072014-140022

Author Xiaoyang Chen
Advisor Karsten Grove
Contributor Karsten Grove, Committee Chair
Contributor Stephan Stolz, Committee Member
Contributor Fred Xavier, Committee Member
Contributor Xiaobo Liu, Committee Member
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name PhD
Defense Date
  • 2014-04-03

Submission Date 2014-04-07
Country
  • United States of America

Subject
  • Fred Wilhelm’s conjecture

  • Riemannian submersions

Publisher
  • University of Notre Dame

Language
  • English

Record Visibility Public
Content License
  • All rights reserved

Departments and Units

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