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

Abstract : 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.
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Submitted on : Thursday, October 3, 2019 - 10:04:43 AM
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Roger Nakad, Julien Roth. Characterization of hypersurfaces in four dimensional product spaces via two different Spin^c structures. 2019. ⟨hal-02304263⟩

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