The Gauss map in spaces of constant curvature
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- by Joel L. Weiner PDF
- Proc. Amer. Math. Soc. 38 (1973), 157-161 Request permission
Abstract:
Let $N$ be a complete simply connected Riemannian manifold of constant sectional curvature $\ne 0$. Let $M$ be an immersed Riemannian hypersurface of $N$. The Gauss map on $M$ based at a point $p$ in $N$ is defined. Suppose a Gauss map on $M$ has constant rank less than the dimension of $M$; then $M$ is generated by Riemannian submanifolds with constant sectional curvature. The sectional curvature of each of these generating submanifolds of $M$ has the same sign as the sectional curvature of $N$.References
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- Ryoichi Takagi, Gauss map in a sphere, K\B{o}dai Math. Sem. Rep. 22 (1970), 82–88. MR 262989
- T. J. Willmore and B. A. Saleemi, The total absolute curvature of immersed manifolds, J. London Math. Soc. 41 (1966), 153–160. MR 185553, DOI 10.1112/jlms/s1-41.1.153
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 157-161
- MSC: Primary 53C40
- DOI: https://doi.org/10.1090/S0002-9939-1973-0310813-6
- MathSciNet review: 0310813