A characterization of differentiable submanifolds of Euclidean spaces
B. Hajduk (1973)
Colloquium Mathematicae
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B. Hajduk (1973)
Colloquium Mathematicae
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J. Witkowski (1963)
Annales Polonici Mathematici
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Carfagna D'Andrea, Antonella (1996)
Beiträge zur Algebra und Geometrie
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Hertrich-Jeromin, Udo (2001)
Balkan Journal of Geometry and its Applications (BJGA)
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Guo Zhen (2004)
Collectanea Mathematica
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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)
Visual Mathematics
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Rolf Schneider (1975)
Annales Polonici Mathematici
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Bashir, M.A. (1991)
International Journal of Mathematics and Mathematical Sciences
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Bashir, M.A. (1995)
International Journal of Mathematics and Mathematical Sciences
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Bashir, M.A. (1994)
International Journal of Mathematics and Mathematical Sciences
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Bang Yen Chen (1972)
Annales Polonici Mathematici
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Matsumoto, Koji, Mihai, Adela, Naitza, Dorotea (2003)
Lobachevskii Journal of Mathematics
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Chuan-Chih Hsiung, Siham Braidi (1970)
Mathematische Zeitschrift
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