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Generalized Sasakian Space Forms Which Are Realized as Real Hypersurfaces in Complex Space Forms
Mathematics, 2020 We prove a classification theorem of the generalized Sasakian space forms which are realized as real hypersurfaces in complex space forms.
Alfonso Carriazo +2 more
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Complex space forms immersed in complex space forms [PDF]
Transactions of the American Mathematical Society, 1976 We determine all the isometric immersions of complex space forms into complex space forms. Our result can be considered as the local version of a well-known result of Calabi.
Nakagawa, H., Ogiue, K.
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Homology groups in CR-warped products of complex space forms [PDF]
HeliyonIn the present paper, by using the result of Lawson-Simons [15], we adopt a different technique to show that there are no stable integral q-currents and a non-trivial homology group in a compact oriented CR-warped product submanifold Nn in a complex ...
Yanlin Li +4 more
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Quasi-Einstein Hypersurfaces of Complex Space Forms
Advances in Mathematical Physics, 2020 Based on a well-known fact that there are no Einstein hypersurfaces in a nonflat complex space form, in this article, we study the quasi-Einstein condition, which is a generalization of an Einstein metric, on the real hypersurface of a nonflat complex ...
Xuehui Cui, Xiaomin Chen
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Kähler maps of Hermitian symmetric spaces into complex space forms
Geometriae Dedicata, 2007 The authors study Kähler immersions of Hermitian symmetric spaces into finite- or infinite-dimensional complex space forms, in particular Kähler immersions of such spaces of noncompact type endowed with their Bergman metrics into the infinite-dimensional hyperbolic space \(\mathbb{C} H^\infty\) or the infinite-dimensional Euclidean space \(\ell^2 ...
Andrea Loi, Antonio José Di Scala
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On the $$\Delta $$-property for complex space forms [PDF]
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 2021 Inspired by the work of Z. Lu and G. Tian [8], A. Loi, F. Salis and F. Zuddas address in [5] the problem of studying those Kähler manifolds satisfying the $Δ$-property, i.e. such that on a neighborhood of each of its points the $k$-th power of the Kähler Laplacian is a polynomial function of the complex Euclidean Laplacian, for all positive integer $k$.
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Differential Geometry of Submanifolds in Complex Space Forms Involving δ-Invariants
Mathematics, 2022 One of the fundamental problems in the theory of submanifolds is to establish optimal relationships between intrinsic and extrinsic invariants for submanifolds.
Bang-Yen Chen +2 more
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CR-SUBMANIFOLDS OF A COMPLEX SPACE FORM [PDF]
Journal of Differential Geometry, 1981 Publisher Summary This chapter presents some fundamental formulas for submanifolds of a Kaehlerian manifold, and in particular for those of a complex space form, and discusses the CR-submanifolds and generic submanifolds. The chapter discusses various theorems related to CR-submanifolds. Theorem 1 is fundamental in the study of CR-submanifolds.
Bejancu, Aurel +2 more
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Vanishing Homology of Warped Product Submanifolds in Complex Space Forms and Applications
Mathematics, 2022 In this paper, we prove the nonexistence of stable integral currents in compact oriented warped product pointwise semi-slant submanifold Mn of a complex space form M˜(4ϵ) under extrinsic conditions which involve the Laplacian, the squared norm gradient ...
Ali H. Alkhaldi +3 more
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δ(2,2)-Invariant for Lagrangian Submanifolds in Quaternionic Space Forms
Mathematics, 2020 In the geometry of submanifolds, Chen inequalities represent one of the most important tool to find relationships between intrinsic and extrinsic invariants; the aim is to find sharp such inequalities. In this paper we establish an optimal inequality for
Gabriel Macsim, Adela Mihai, Ion Mihai
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