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Slant immersions

Published online by Cambridge University Press:  17 April 2009

Bang-Yen Chen
Bang-Yen Chen
Affiliation:
Department of Mathematics, Michigan State University, East Lansing MI 48824, United States of America.
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Abstract

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A slant immersion is defined as an isometric immersion from a Riemannnian manifold into an almost Hermitian manifold with constant Wirtinger angle. In this article we give some fundamental results concerning slant immersions. Several results on slant surfaces in ℂ2 are also proved.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 1 , February 1990 , pp. 135 - 147
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Chen, B.Y., Geometry of Submanifolds (Dekker, New York, 1973).Google Scholar
[2]Chen, B.Y., ‘Differential geometry of real submanifolds in a Kähler manifold’, Monatsh. Math. 91 (1981), 257–274.CrossRefGoogle Scholar
[3]Chen, B.Y. and Ogiue, K., ‘On totally real sudmanifolds’, Trans. Amer. Math. Soc. 193 (1974), 257–266.CrossRefGoogle Scholar
[4]Chen, B.Y. and Morvan, J.M., ‘Propriété riemanniennes des surfaces lagrangiennes’, C.R. Acad. Sci. Paris. Ser I 301 (1985), 209–212.Google Scholar
[5]Chen, B.Y. and Morvan, J.M., ‘Geometrie des surfaces lagrangiennes de ℂ2’, J. Math. Pures Appl. 66 (1987), 321–335.Google Scholar
[6]Gheysens, L., Verheyen, P. and Verstraelen, L., ‘Characterization and examples of Chen submanifolds’, J. Geom. 20 (1983), 47–62.CrossRefGoogle Scholar
[7]Lashof, R.K. and Smale, S., ‘On the immersion of manifolds in Euclidean spaces’, Ann. of Math. 68 (1958), 562–583.CrossRefGoogle Scholar
[8]Lawson, H.B., Lectures on Minimal Submanifolds (Publish or Perish, Berkeley, 1980).Google Scholar
[9]Little, J.A., ‘On singularities of surfaces in E 4’, Bull. Amer. Math. Soc. 75 (1969), 368–369.CrossRefGoogle Scholar