Bakry-Émery Ricci Curvature on Manifolds with Boundary

• Author / Creator

  Moore, Kenneth

• A classic result in the field of Riemannian Geometry is the Splitting Theorem of Cheeger and Gromoll. Since this result there have been numerous alternate versions under a variety of different conditions. Continuing in this vein, we prove structure results on manifolds with boundary components under m-Bakry-Émery Ricci curvature bounds. First we look at a generalization of Frankel’s theorem [9], extrapolating on the work of Peterson and Wilhelm [25]. We then prove some related corollaries that were shown by Choe and Fraser [4]. Finally we generalize the splitting theorems of Sakurai [28], [29] for manifolds with boundary and a non-gradient vector field.

• Subjects / Keywords

  • Riemannian Geometry
  • Differential Geometry
  • Splitting
  • manifolds with boundary
  • Bakry-Émery Ricci

• Graduation date

  Fall 2021

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-8x7g-g239

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.