Proceedings of the American Mathematical Society · 1976 · 58 citations · 2 references
Natural SciencesMathematicsGeometryDifferential GeometryMetric GeometryRiemannian GeometryConnections On ManifoldsCurvature OperatorLevi-civita ConnectionRicci CurvatureRiemannian MetricSubmanifold Theory
We derive the Gauss curvature equation and the Codazzi-Mainardi equation with respect to a semisymmetric metric connection on a Riemannian manifold and the induced one on a submanifold. We then generalize the theorema egregium of Gauss.
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INTEGRAL FORMULAS IN RIEMANNIAN GEOMETRY
T. J. Willmore · Bulletin of the London Mathematical Society · 1973 · 310 citations