Submanifolds of framed metric manifolds and S-manifolds


Abstract


Almost semi-invariant submanifolds of framed metric manifolds and S-manifolds are studied, where the ambient manifolds generalize almostHermitian, Kaehler, almost contact metric and Sasakian manifolds while thesubmanifolds generalize/imply several known classes of submanifoldsincluding CR, semi-invariant, holomorphic, totally real and slantsubmanifolds. Integrability conditions for certain natural distributions onalmost semi-invariant submanifolds of S-manifolds are investigated.Parallelism of the operators arising naturally in the study is investigatedleading to a flowchart connecting them. Totally umbilical, totally geodesicand totally contact geodesic submanifolds are studied. Some relationsbetween almost semi-invariant submanifolds of a framed metric manifold andother submanifolds are investigated. Submanifolds of principal toroidalbundles are also studied.


DOI Code: 10.1285/i15900932v20n2p135

Keywords: Framed metric manifold; S-manifold and S-space form; CR; Semi-invariant; Almost semi-invariant; Holomorphic; Totally real and slant submanifolds; Totally contact geodesic submanifold; Tangent bundle and principal toroidal bundle

Classification: 53C15; 53C40; 53C42

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