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The characterization of totally geodesic submanifolds ofS m andCP m

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Abstract

We prove a theorem on ruled surfaces that generalizes a theorem of Ferus on totally geodesic foliations. On the basis of this theorem we obtain criteria for totally geodesic submanifolds ofS m andCP m that generalize and complement certain results of Borisenko, Ferus, and Abe. We give an application to the geodesic differential forms defined by Dombrowski in the case of submanifolds ofS m andCP m.

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Literature cited

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Authors
  1. V. Yu. Rovenskií
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Additional information

Translated from Ukrainskií Geometricheskií Sbornik, Issue 28, 1985, pp. 106–116.

The author is grateful to V. A. Toponogov for posing this problem and for attention to the work and to A. A. Borisenko for helpful criticisms.

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Rovenskií, V.Y. The characterization of totally geodesic submanifolds ofS m andCP m . J Math Sci 48, 87–94 (1990). https://doi.org/10.1007/BF01098051

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  • DOI: https://doi.org/10.1007/BF01098051

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