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CR-Submanifolds of the Nearly Kähler 6-Sphere
, 2016 International audienceThere is an almost complex structure J on the sphere S6(1) defined by multiplication of the Cayley numbers. This structure is nearly Kähler. A submanifold of a manifold with an almost complex structure is CR, by Bejancu, if it has a
Luc Vrancken +3 more
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CR submanifolds in Kaehler and nearly Kaehler manifolds [PDF]
, 2004 A review of the study of CR, submanifolds within Kaehler and nearly Kaehler manifolds, and the properties of such manifolds with respect submanifold theory in differential geometry.
Gregg, Matthew Thomas
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A Frankel type theorem for CR submanifolds of Sasakian manifolds [PDF]
, 2023 We prove a Frankel type theorem for CR submanifolds of Sasakian manifolds, under suitable hypothesis on the index of the scalar Levi forms determined by normal directions.
Dario Di Pinto +3 more
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Inflexible CR submanifolds [PDF]
Mathematische Zeitschrift, 2016 to appear in Math ...
Brinkschulte, Judith, Denson Hill, C.
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Homology of contact CR-submanifolds
Filomat, 2021 In this paper, homology of a contact CR-submanifold of a real hypersurface, which has naturally almost contact metric structure induced from the complex Euclidean space Cm, is examined. More precisely, nonexistence of stable integral currents on a compact contact CR-submanifold of real hypersurface of canonical complex space form Cm is ...
Sahin, Fulya, Sahin, Bayram
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Kodai Mathematical Journal, 1982 Let \(\bar M\) be a (2m+1)-dimensional Sasakian manifold with structure tensors (φ,ξ,η,g). We consider a Riemannian manifold isometrically immersed in \(\bar M\) with induced metric tensor field g.
Yano, Kentaro, Kon, Masahiro
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Flatness of CR submanifolds in a sphere [PDF]
Science China Mathematics, 2010 Let $M$ be the image of a smooth CR embedding of a strictly pseudoconvex CR real hypersurface into a sphere. If the CR second fundamental form of $M$ vanishes, we show that $M$ is a totally geodesic submanifold.
Ji, Shanyu, Yuan, Yuan
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THE NORMAL HOLONOMY OF CR-SUBMANIFOLDS [PDF]
Osaka Journal of Mathematics, 2017 We study the normal holonomy group, i.e. the holonomy group of the normal connection, of a $CR$-submanifold of a complex space form. We show that the normal holonomy group of a coisotropic submanifold acts as the holonomy representation of a Riemannian symmetric space.
DI SCALA, ANTONIO JOSE' +1 more
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Submersions of {CR} submanifolds [PDF]
Tohoku Mathematical Journal, 1987 A real submanifold N of a complex Banach manifold V is called a CR submanifold if \(T^ h=TN\cap J(TN)\) is a complex subbundle of the tangent bundle TV; J being the relevant complex structure. Assume V Kähler, let \(T^{\vee}N\) be the orthogonal complement of \(T^ hN\) in TN, \(T^ nN\) be the normal bundle. Assume that J interchanges \(T^{\vee}N\) and \
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Minimal homogeneous submanifolds in euclidean spaces [PDF]
, 2002 We prove that minimal (extrinsically) homogeneous submanifolds of the Euclidean space are totally geodesic. As an application, we obtain that a complex (intrisecally) homogeneous submanifold of a complex Euclidean space must be totally ...
Di Scala, Antonio Jose'
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