Results 21 to 30 of about 2,185 (102)
On CR‐submanifolds of the six‐dimensional sphere
International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 1, Page 201-203, 1995., 1995 We consider proper CR‐submanifolds of the six‐dimensional sphere S6. We prove that S6 does not admit compact proper CR‐submanifolds with non‐negative sectional curvature and integrable holomorphic distribution.
M. A. Bashir
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Orientations and Geometrisations of Compact Complex Surfaces
, 1997 Every complex manifold carries a canonical orientation, and it is natural to wonder when the underlying topological or smooth manifold carries a complex structure compatible with the other orientation.
D. Kotschick
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CR‐hypersurfaces of the six‐dimensional sphere
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 1, Page 197-200, 1994., 1994 We proved that there does not exist a proper CR‐hypersurface of S6 with parallel second fundamental form. As a result of this we showed that S6 does not admit a proper CR‐totally umbilical hypersurface. We also proved that an Einstein proper CR‐hypersurface of S6 is an extrinsic sphere.
M. A. Bashir
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Kähler metrics via Lorentzian Geometry in dimension four
Complex Manifolds, 2019 Given a semi-Riemannian 4-manifold (M, g) with two distinguished vector fields satisfying properties determined by their shear, twist and various Lie bracket relations, a family of Kähler metrics gK is constructed, defined on an open set in M, which ...
Aazami Amir Babak, Maschler Gideon
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CR‐hypersurfaces of complex projective space
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 3, Page 613-616, 1994., 1994 We consider compact n‐dimensional minimal foliate CR‐real submanifolds of a complex projective space. We show that these submanifolds are great circles on a 2‐dimensional sphere provided that the square of the length of the second fundamental form is less than or equal to n − 1.
M. A. Bashir
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Contact manifolds, Lagrangian Grassmannians and PDEs
Complex Manifolds, 2018 In this paper we review a geometric approach to PDEs. We mainly focus on scalar PDEs in n independent variables and one dependent variable of order one and two, by insisting on the underlying (2n + 1)-dimensional contact manifold and the so-called ...
Eshkobilov Olimjon +3 more
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A characterization of finite vector bundles on Gauduchon astheno-Kahler manifolds [PDF]
Épijournal de Géométrie Algébrique, 2018 A vector bundle E on a projective variety X is called finite if it satisfies a nontrivial polynomial equation with integral coefficients. A theorem of Nori implies that E is finite if and only if the pullback of E to some finite etale Galois covering of ...
Indranil Biswas, Vamsi Pritham Pingali
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Stenzel's Ricci-flat Kaehler metrics are not projectively induced [PDF]
, 2020 We investigate the existence of a holomorphic and isometric immersion in the complex projective space for the complete Ricci-flat Kaehler metrics constructed by M. B.
Zedda, Michela
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EXISTENCE AND COMPACTNESS THEORY FOR ALE SCALAR-FLAT KÄHLER SURFACES
Forum of Mathematics, Sigma, 2020 Our main result in this article is a compactness result which states that a noncollapsed sequence of asymptotically locally Euclidean (ALE) scalar-flat Kähler metrics on a minimal Kähler surface whose Kähler classes stay in a compact subset of the ...
JIYUAN HAN, JEFF A. VIACLOVSKY
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New representation of the non‐symmetric homogeneous bounded domains in ℂ4 and ℂ5
International Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 4, Page 741-752, 1992., 1990 This paper deals with the corresponding solvable Lie algebra to each of non‐symmetric homogeneous bounded domains in ℂ4 and ℂ5 by special set of matrices. Some interesting properties of Kähler manifolds are found. The theory of s‐structure on a complete Riemann manifold is also studied.
Gr. Tsagas, G. Dimou
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