Notes on Conformal Metrics of Negative Curvature on Manifolds with Boundary

Authors

  • Rirong Yuan

DOI:

https://doi.org/10.4208/jms.v57n3.24.08

Keywords:

Schouten tensor, Modified Schouten tensor, conformal deformation, Morse theory.

Abstract

We use certain Morse functions to construct conformal metrics such that the eigenvalue vector of modified Schouten tensor belongs to a given cone. As a result, we prove that any Riemannian metric on compact 3-manifolds with boundary is conformal to a compact metric of negative sectional curvature.

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Published

2024-10-31

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Issue

Vol. 57 No. 3 (2024)

Section

Articles

How to Cite

Notes on Conformal Metrics of Negative Curvature on Manifolds with Boundary. (2024). Journal of Mathematical Study, 57(3), 373-378. https://doi.org/10.4208/jms.v57n3.24.08