Kodai Mathematical Journal

On the existence of spherically bent submanifolds, an analogue of a theorem of E. Cartan

Knut Pawel and Helmut Reckziegel

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Abstract

In this article an analogue of E. Cartan's theorem about the existence of (local) totally geodesic submanifolds with a prescribed tangent plane is proved, namely for the existence of spherically bent submanifolds (= extrinsic spheres); also a global version is deduced.

Article information

Source
Kodai Math. J., Volume 26, Number 2 (2003), 199-220.

Dates
First available in Project Euclid: 26 August 2003

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1061901062

Digital Object Identifier
doi:10.2996/kmj/1061901062

Mathematical Reviews number (MathSciNet)
MR2004e:53084

Zentralblatt MATH identifier
1053.53014

Citation

Pawel, Knut; Reckziegel, Helmut. On the existence of spherically bent submanifolds, an analogue of a theorem of E. Cartan. Kodai Math. J. 26 (2003), no. 2, 199--220. doi:10.2996/kmj/1061901062. https://projecteuclid.org/euclid.kmj/1061901062


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