Some scalar curvature warped product splitting theorems

Gregory J. Galloway; Hyun Chul Jang

Some scalar curvature warped product splitting theorems

Differential Geometry 2019-10-31 v2 General Relativity and Quantum Cosmology

Authors: Gregory J. Galloway , Hyun Chul Jang

Abstract

We present several rigidity results for Riemannian manifolds $(M^n,g)$ with scalar curvature $S \ge -n(n-1)$ (or $S\ge 0$ ), and having compact boundary $N$ satisfying a related mean curvature inequality. The proofs make use of results on marginally outer trapped surfaces applied to appropriate initial data sets. One of the results involves an analysis of Obata's equation on manifolds with boundary. This result is relevant to recent work of Lan-Hsuan Huang and the second author concerning the rigidity of asymptotically locally hyperbolic manifolds with zero mass.

Keywords

scalar curvature warped product rigidity mean curvature marginally outer trapped surfaces obata equation asymptotically locally hyperbolic manifolds

Cite

@article{arxiv.1907.09396,
  title  = {Some scalar curvature warped product splitting theorems},
  author = {Gregory J. Galloway and Hyun Chul Jang},
  journal= {arXiv preprint arXiv:1907.09396},
  year   = {2019}
}

Comments

15 pages; v2: Introduction revised, other small changes; results unchanged. To appear in Proc. Amer. Math. Soc

Some scalar curvature warped product splitting theorems

Abstract

Keywords

Cite

Comments

Related papers