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Alegre, Pablo; Chen, Bang-Yen; Munteanu, Marian Ioan

Riemannian submersions, \(\delta\)-invariants, and optimal inequality. (English) Zbl 1253.53057

Ann. Global Anal. Geom. 42, No. 3, 317-331 (2012).
Summary: We establish a sharp relation between \(\delta\)-invariants and Riemannian submersions with totally geodesic fibers. By using this relationship, we establish an optimal inequality involving \(\delta\)-invariants for submanifolds of the complex projective space \(\mathbb CP ^{m}(4)\) via Hopf’s fibration \({\pi:S^{2m+1}\to\mathbb CP^{m}(4)}\). Moreover, we completely classify the submanifolds of the complex projective space which satisfy the equality case of the inequality.

Cited in 27 Documents

MSC:

53C40 Global submanifolds
53B25 Local submanifolds
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)

Keywords:

Riemannian submersion; \(\delta\)-invariant; optimal inequality; totally real submanifold; \(CR\)-submanifold
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References:

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