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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Extremal length in higher dimensions and complex systolic inequalities [PDF]
, 2020 Extremal length is a classical tool in 1-dimensional complex analysis for building conformal invariants. We propose a higher-dimensional generalization for complex manifolds and provide some ideas on how to estimate and calculate it.
Pacini, Tommaso
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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 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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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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Some examples of special Lagrangian tori
, 1999 I point out some very elementary examples of special Lagrangian tori in certain Calabi-Yau manifolds that occur as hypersurfaces in complex projective space. All of these are constructed as real slices of smooth hypersurfaces defined over the reals. This
Bryant, Robert L.
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, 2009 We first review the notion of a $G_2$-manifold, defined in terms of a principal $G_2$ ("gauge") bundle over a $7$-dimensional manifold, before discussing their relation to supergravity. In a second thread, we focus on associative submanifolds and present
Frederik Witt +4 more
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Intersections of quadrics, moment-angle manifolds, and Hamiltonian-minimal Lagrangian embeddings
, 2013 We study the topology of Hamiltonian-minimal Lagrangian submanifolds N in C^m constructed from intersections of real quadrics in a work of the first author.
A Amarzaya +29 more
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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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