The differential geometry of CR submanifolds of a Kaehler manifold is studied. Theorems about totally geodesic CR submanifolds and totally umbilical CR submanifolds are given.

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Aurel Bejancu (Sat,) studied this question.

synapsesocial.com/papers/6a0f6bcf92676d5461fcb0d7 https://doi.org/https://doi.org/10.1090/s0002-9939-1978-0467630-0

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1Geometry of submanifolds1973 · 893 citations
2Foundations of Differential Geometry1963 · 6,236 citations
3On a structure defined by a tensor field f of type (1, 1) satisfying f^3+f=01963 · 148 citations
4Approximation theorems on differentiable submanifolds of a complex manifold1969 · 84 citations
5Totally real submanifolds of complex space forms. II.1976 · 17 citations

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1Geometry of submanifolds1973 · 893 citations
2Foundations of Differential Geometry1963 · 6,236 citations
3On a structure defined by a tensor field f of type (1, 1) satisfying f^3+f=01963 · 148 citations
4Approximation theorems on differentiable submanifolds of a complex manifold1969 · 84 citations
5Totally real submanifolds of complex space forms. II.1976 · 17 citations