Browsing by Author "Mihai, Ion"
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Item Certain inequalities for submanifolds in (K, mu)-contact space forms(Cambridge Univ. Press, 2001-10) Mihai, Ion; Arslan, Kadri; Ezentaş, Rıdvan; Murathan, Cengizhan; Cihan, Özgür; Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0003-3782-2983; A-1671-2008; ABH-3658-2020; ABE-8167-2020; 6603079141; 6506973222; 6506718146; 15924108200Chen (1999) established a sharp relationship between the Ricci curvature and the squared mean curvature for a submanifold in a Riemanian space form with arbitrary codimension. Matsumoto (to appear) dealt with similar problems for submanifolds in complex space forms. In this article we obtain sharp relationships between the Ricci curvature and the squared mean curvature for submanifolds in (k,mu)-contact space forms.Item Contact CR-warped product submanifolds in Kenmotsu space forms(Korean Mathematical Soc, 2005-09) Mihai, Ion; Arslan, Kadri; Ezentaş, Rıdvan; Murathan, Cengizhan; Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0001-5861-0184; 0000-0002-1440-7050; ABH-3658-2020; AAG-8775-2021Recently, Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. In the present paper, we obtain sharp estimates for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Kenmotsu space forms. The equality case is considered. Some applications are derived.Item Warped product submanifolds in Kenmotsu space forms(Mathematical Society Republic of China, 2006-12) Mihai, Ion; Murathan, Cengizhan; Arslan, Kadri; Ezentaş, Rıdvan; Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-1440-7050; 0000-0001-5861-0184; ABH-3658-2020; AAG-8775-2021; 6602927353Recently, Chen established a general sharp inequality for warped products in real space forms. As applications, he obtained obstructions to minimal isometric immersions of warped products into real space forms. Afterwards, Matsumoto and one of the present authors proved the Sasakian version of this inequality. In the present paper, we obtain sharp estimates for the warping function in terms of the mean curvature for warped products isometrically immersed in Kenmotsu space forms. Some applications are derived.