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On a relation between the topology and the intrinsic and extrinsic geometries of a compact submanifold
Let M n be an n -dimensional smooth compact Riemannian manifold. By a theorem of Nash, we can think of it as an isometrically immersed submanifold in some higher dimensional Euclidean space ℝ n + m . Viewing in this way we can compare the intrinsic geometry of M to …