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Bulletin of the Australian Mathematical Society Bulletin of the Australian Mathematical Society

Article contents

Convolution of Riemannian manifolds and its applications

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 48824–1027, United States of America e-mail: bychen@math.msu.edu
Corresponding
E-mail address:
bychen@math.msu.edu
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Extract

It is well-known that warped products play some important roles in differential geometry as well as in physics. In this article we extend the notion of warped product to the notion of convolution of Riemannian manifolds. We study the basic properties of convolutions of Riemannian manifolds. We also apply the notion of convolution to establish and characterise the Euclidean version of Segre embedding.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 66 , Issue 2 , October 2002 , pp. 177 - 191
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Bejancu, A., Geometry of CR-Submanifolds, Mathematics and its Applications 23 (D. Reidel Publishing Co., Dordrecht, 1986).CrossRefGoogle Scholar
[2]Chen, B.Y., ‘Some CR-submanifolds of a Kaehler manifold. I’, J. Differential Geom. 16 (1981), 305–322.CrossRefGoogle Scholar
[3]Chen, B.Y., ‘Some CR-submanifolds of a Kaehler manifold. II’, J. Differential Geom. 16 (1981), 493–509.CrossRefGoogle Scholar
[4]Chen, B.Y., ‘Geometry of warped product CR-submanifolds in Kaehler manifolds’, Monatsh. Math. 133 (2001), 177–195.CrossRefGoogle Scholar
[5]Chen, B.Y., ‘Geometry of warped products CR-submanifolds in Kaehler manifolds. II’, Monatsh. Math. 134 (2001), 103–119.CrossRefGoogle Scholar
[6]Chen, B.Y., ‘More on convolution of Riemannian manifolds’, Beiträge Algebra Geom. (to appear).Google Scholar
[7]O'Neill, B., Semi-Riemannian geometry with applications to relativity, Pure and Applied Mathematics 103 (Academic Press, New York, 1983).Google Scholar

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