Geometry of pointwise CR-slant warped products in Kaehler manifolds

• Bang-Yen Chen ^[1] ; Siraj Uddin ^[2] ; Falleh R. Al-Solamy ^[2]
  1. [1] Michigan State University

     Michigan State University

     City of East Lansing, Estados Unidos

     
  2. [2] King Abdulaziz University

     King Abdulaziz University

     Arabia Saudí

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 61, Nº. 2, 2020, págs. 353-365
• Idioma: inglés
• DOI: 10.33044/revuma.v61n2a11
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• Resumen

  • We call a submanifold M of a Kaehler manifold M˜ a pointwise CR-slant warped product if it is a warped product, B ×f Nθ, of a CR-product B = NT × N⊥ and a proper pointwise slant submanifold Nθ with slant function θ, where NT and N⊥ are complex and totally real submanifolds of M˜ . We prove that if a pointwise CR-slant warped product B×f Nθ with B = NT ×N⊥ in a Kaehler manifold is weakly Dθ -totally geodesic, then it satisfies kσk 2 ≥ 4s (csc2θ + cot2θ)k∇T(ln f)k2 + (cot2θ)k∇⊥(ln f)k2, where NT , N⊥, and Nθ are complex, totally real and proper pointwise slant submanifolds of M˜ , respectively, and s = 1/ 2 dim Nθ. In this paper we also investigate the equality case of the inequality. Moreover, we give a non-trivial example and provide some applications of this inequality.