Simons' Type Formula for Kaehlerian Slant Submanifolds in Complex Space Forms

Simons' Type Formula for Kaehlerian Slant Submanifolds in Complex Space Forms

A. Bejancu [2] was the first who instigated the new concept in differential geometry, i.e., CR-submanifolds. On the other hand, CR-submanifolds were generalized by B. Y. Chen [7] as slant submanifolds. Further, he gave the notion of a Kaehlerian slant submanifold as a proper slant submanifold. This...

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Veröffentlicht in:Kyungpook mathematical journal 2018, Vol.58 (1), p.149-165
Hauptverfasser: Siddiqui, Aliya Naaz, Shahid, Mohammad Hasan, Jamali, Mohammed
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Shahid, Mohammad Hasan
Jamali, Mohammed
description A. Bejancu [2] was the first who instigated the new concept in differential geometry, i.e., CR-submanifolds. On the other hand, CR-submanifolds were generalized by B. Y. Chen [7] as slant submanifolds. Further, he gave the notion of a Kaehlerian slant submanifold as a proper slant submanifold. This article has two objectives. For the first objective, we derive Simons' type formula for a minimal Kaehlerian slant submanifold in a complex space form. Then, by applying this formula, we give a complete classification of a minimal Kaehlerian slant submanifold in a complex space form and also obtain its some immediate consequences. The second objective is to prove some results about semi-parallel submanifolds.
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title Simons' Type Formula for Kaehlerian Slant Submanifolds in Complex Space Forms
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