A characterization of differentiable submanifolds of Euclidean spaces
B. Hajduk (1973)
Colloquium Mathematicae
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B. Hajduk (1973)
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J. Witkowski (1963)
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Hertrich-Jeromin, Udo (2001)
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In this paper we generalize the self-adjoint differential operator (used by Cheng-Yau) on hypersurfaces of a constant curvature manifold to general submanifolds. The generalized operator is no longer self-adjoint. However we present its adjoint operator. By using this operator we get the pinching theorem on Willmore submanifolds which is analogous to the pinching theorem on minimal submanifold of a sphere given by Simon and Chern-Do Carmo-Kobayashi.
John M. Sullivan (1999)
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Rolf Schneider (1975)
Annales Polonici Mathematici
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Bashir, M.A. (1991)
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Bashir, M.A. (1995)
International Journal of Mathematics and Mathematical Sciences
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Bashir, M.A. (1994)
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