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Differential Geometry of Identity Maps: A Survey

Author

Listed:
  • Bang-Yen Chen

    (Department of Mathematics, Michigan State University, 619 Red Cedar Road, East Lansing, MI 48824-1027, USA)

Abstract

An identity map i d M : M → M is a bijective map from a manifold M onto itself which carries each point of M return to the same point. To study the differential geometry of an identity map i d M : M → M , we usually assume that the domain M and the range M admit metrics g and g ′ , respectively. The main purpose of this paper is to provide a comprehensive survey on the differential geometry of identity maps from various differential geometric points of view.

Suggested Citation

  • Bang-Yen Chen, 2020. "Differential Geometry of Identity Maps: A Survey," Mathematics, MDPI, vol. 8(8), pages 1-32, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1264-:d:393409
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