Characterization of hypersurfaces in four dimensional product spaces via two different Spin^c structures

The Riemannian product M1(c1)×M2(c2), where Mi(ci) denotes the 2-dimensional space form of constant sectional curvature ci ∈ R, has two different Spin c structures carrying each a parallel spinor. The restriction of these two parallel spinor fields to a 3-dimensional hypersurface M characterizes the...

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Bibliographic Details
Published in:Annals of global analysis and geometry Vol. 61; no. 1; pp. 89 - 114
Main Authors: Nakad, Roger, Roth, Julien
Format: Journal Article
Language:English
Published: Springer Verlag 07.10.2021
Subjects:
Differential Geometry
Mathematics
53C40
totally umbilcal hypersurfaces
Kähler manifolds Mathematics subject classifications : 53C27
generalized Killing Spin c spinors
parallel Spin c spinors
Spin c structures on hypersurfaces
53C80
ISSN:0232-704X, 1572-9060
Online Access:Get full text
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Summary:The Riemannian product M1(c1)×M2(c2), where Mi(ci) denotes the 2-dimensional space form of constant sectional curvature ci ∈ R, has two different Spin c structures carrying each a parallel spinor. The restriction of these two parallel spinor fields to a 3-dimensional hypersurface M characterizes the isometric immersion of M into M1(c1) × M2(c2). As an application, we prove that totally umbilical hypersurfaces of M1(c1) × M1(c1) and totally umbilical hypersurfaces of M1(c1) × M2(c2) (c1 = c2) having a local structure product, are of constant mean curvature.
ISSN:0232-704X
1572-9060
DOI:10.1007/s10455-021-09802-4