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Suppose that in a coordinate patch x: U M the Weingarten map satisfies L = fI where f : U R and I is the

Suppose that in a coordinate patch x: U M the Weingarten map satisfies L = fI where f : U R and I is the identity linear transformation. Prove that f is a constant in a neighborhood of each point.

elements of differential geometry george d. parker page137 8.14

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