Differential Geometry of Identity Maps: A Survey

Bang-Yen Chen
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Bang-Yen Chen: Department of Mathematics, Michigan State University, 619 Red Cedar Road, East Lansing, MI 48824-1027, USA

Mathematics, 2020, vol. 8, issue 8, 1-32

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.

Keywords: identity map; harmonic map; biharmonic map; Gauss map; Laplace map; harmonic metrics; Walker manifold; Gödel-type space time; index; nullity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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