Izvestiya: Mathematics, 1995 Summary: Let \(X\) be a complex manifold, \(M\subset X\) a (closed, oriented) real submanifold, and \(S\subset M\) the set of \(\mathbb{R}\mathbb{C}\)-singular points of \(M\). We study the connection between the global topological characteristics of \(S\) and the topology of \(M\) and \(X\).
A V Domrin
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The Dimension Function of Holomorphic Spaces of a Real Submanifold of an Almost Complex Manifold [PDF]
Czechoslovak Mathematical Journal, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Etayo, Fernando +2 more
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The Hodge conjecture: The complications of understanding the shape of geometric spaces
Mètode Science Studies Journal: Annual Review, 2018 The Hodge conjecture is one of the seven millennium problems, and is framed within differential geometry and algebraic geometry. It was proposed by William Hodge in 1950 and is currently a stimulus for the development of several theories based on ...
Vicente Muñoz Velázquez
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Real analytic manifolds in
Annales de la Faculté des sciences de Toulouse : Mathématiques, 2009 We will classify n -dimensional real submanifolds in ℂ n
Patrick Ahern, Xianghong Gong
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On real submanifolds of Kähler manifolds foliated by complex submanifolds
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1994 Let \(X\) be a Kähler manifold, \(M\) a compact orientable real submanifold of \(X\), and suppose that \(M\) admits a foliation \(\mathfrak F\) whose leaves are complex submanifolds of \(X\) with complex dimension \(p\). The authors prove that if the \(p\)-th power of the Kähler form of \(X\) is exact when restricted to \(M\), then \(\mathfrak F\) has ...
Inaba, Takashi, Mishchenko, Michael A.
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Real-analytic submanifolds of complex manifolds [PDF]
Proceedings of the American Mathematical Society, 1971 This paper examines the extendibility of holomorphic functions on a real manifold which is embedded in a complex manifold. The principal result is that all real k-dimensional, real-analytic, compact manifolds embedded in an n-dimersional complex Stein manifold, where k >n, are extendible over a manifold of one higher real dimension.
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Lectures given at the C.I.M.E. Summer School
, 2004 The geometry of real submanifolds in complex manifolds and the analysis of their mappings belong to the most advanced streams of contemporary Mathematics. In this area converge the techniques of various and sophisticated mathematical fields such as P.D.E.
Zaitsev, Dmitri, Zampieri, Giuseppe
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Kähler submanifolds of real and complex Riemannian manifolds
Matemática Contemporânea, 1993 The purpose of this article is to present some inequalities involving the type component \(\alpha^{(1,1)}\) of the second fundamental form \(\alpha\) of a Kähler submanifold and give geometric interpretations to the cases where the equalities hold. Moreover, since the parallelism of \(\alpha^{(1,1)}\) is equivalent, in the case of surfaces, to the ...
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Unfolding CR Singularities [PDF]
, 2010 A notion of unfolding, or multi-parameter deformation, of CR singularities of real submanifolds in complex manifolds is proposed, along with a definition of equivalence of unfoldings under the action of a group of analytic transformations.
Adam Coffman, Coffman, Adam
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Unfolding CR Singularities of Real 4-manifolds in C5
, 2007 A notion of unfolding, or multi-parameter deformation, of CR singularities of real submanifolds in complex manifolds is proposed, along with a definition of equivalence of unfoldings under the action of a group of analytic transformations. In the case of
Coffman, Adam
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