Abstract
In this paper CR-warped product submanifolds of a generalized complex space form are studied and a characterizing inequality for existence of CR-warped product submanifolds is established. Moreover, some special cases are also discussed.
Highlights
The notion of warped product of manifolds was introduced by Bishop and O’Neill (1965) in order to construct a large velocity of manifolds of negative curvature
2011, 2013) investigated an inequality for squared norm of second fundamental form which characterize the existence of contact CR-warped product submanifolds in the setting of Cosymplectic and Kenmotsu space forms
For a warped product manifold N1 × N2, we denote by D1 and D2 the distributions defined by the vectors tangent to the leaves and fibers respectively
Summary
The notion of warped product of manifolds was introduced by Bishop and O’Neill (1965) in order to construct a large velocity of manifolds of negative curvature. Chen considered the warped product of the type NT ×f N⟂, and obtained an inequality for squared norm of second fundamental form, these types of warped product are called CR-warped product. In Al-Luhaibi, Al-Solamy, and Khan (2009) investigated CR-warped product submanifolds in the setting of nearly Kaehler manifolds and obtained some basic results and worked out an estimation for squared norm of second fundamental form if ambient manifold is generalized complex space form. These types of warped products are studied in different settings of almost Hermitian manifolds These types of warped products are studied in different settings of almost Hermitian manifolds (c.f. Al-Luhaibi et al, 2009; Faghfouri & Majidi, 2015; Khan & Jamal, 2010; Sahin, 2009)
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