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Ideal CR submanifolds in non-flat complex space forms. (English) Zbl 1340.53088

Summary: An explicit representation for ideal CR submanifolds of a complex hyperbolic space has been derived in [the author, Tsukuba J. Math. 26, No. 1, 119–132 (2002; Zbl 1129.53302)]. We simplify and reformulate the representation in terms of certain Kähler submanifolds. In addition, we investigate the almost contact metric structure of ideal CR submanifolds in a complex hyperbolic space. Moreover, we obtain a codimension reduction theorem for ideal CR submanifolds in a complex projective space.

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53B25 Local submanifolds

Citations:

Zbl 1129.53302
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References:

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[9] T. Sasahara: On Chen invariant of CR-submanifolds in a complex hyperbolic space. Tsukuba J. Math. 26 (2002), 119–132. · Zbl 1129.53302
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