Study on the finiteness of the fundamental groups of Lorentzian manifolds

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K17537
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Toyota Technological Institute (2017); Nagoya University (2015-2016)
• Principal Investigator: MUKUNO Junichi 豊田工業大学, 工学部, ポストドクトラル研究員 (50737301)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: マイヤースの定理 / 特異点定理 / 不定値計量 / 基本群 / 測地的完備性 / 曲率テンソル

Outline of Final Research Achievements

I have studied whether or not for Lorentzian geometry, and in general pseudo-Riemannian geometry, the positivity of curvature tensor and the geodesic completeness lead to the finiteness of the fundamental group. This is to research an analogy of the Myers theorem in pseudo-Riemannian geometry. I have found that if classes of geodesically complete Lorentzian manifolds and pseudo-Riemannian manifolds have the positivity of curvature tensor, then the fundamental group of some Riemannian submanifold of maximal dimension is finite. I have constructed new examples of pseudo-Riemannian homogeneous spaces with the positivity of curvature tensor.

Free Research Field

微分幾何学