Relative nullity distributions, an affine immersion from an almost product manifold and a para-pluriharmonic isometric immersion

2012 ◽  
Vol 42 (3) ◽  
pp. 333-347
Author(s):  
Sanae Kurosu
Keyword(s):  
Isometric Immersion ◽  
Product Manifold ◽  
Relative Nullity ◽  
Affine Immersion ◽  
Almost Product Manifold

scholarly journals SOME CONSTRUCTIONS OF ALMOST PARA-HYPERHERMITIAN STRUCTURES ON MANIFOLDS AND TANGENT BUNDLES

2008 ◽  
Vol 05 (06) ◽  
pp. 893-903 ◽  
Author(s):  
STERE IANUŞ ◽  
GABRIEL EDUARD VÎLCU
Keyword(s):  
Tangent Bundle ◽  
Product Manifold ◽  
Circle Bundle ◽  
Almost Product Manifold ◽  
Tangent Bundles

In this paper we give some examples of almost para-hyperhermitian structures on the tangent bundle of an almost product manifold, on the product manifold M × ℝ, where M is a manifold endowed with a mixed 3-structure and on the circle bundle over a manifold with a mixed 3-structure.

scholarly journals NATURAL CONNECTION WITH TOTALLY SKEW-SYMMETRIC TORSION ON RIEMANNIAN ALMOST PRODUCT MANIFOLDS

2012 ◽  
Vol 09 (01) ◽  
pp. 1250003 ◽  
Author(s):  
DIMITAR MEKEROV ◽  
MANCHO MANEV
Keyword(s):  
Linear Connection ◽  
Riemannian Metric ◽  
Sufficient Condition ◽  
Product Manifold ◽  
Necessary And Sufficient Condition ◽  
Natural Connection ◽  
Almost Product Manifold ◽  
Hermitian Geometry ◽  
Levi Civita Connection ◽  
Necessary And Sufficient

On a Riemannian almost product manifold (M, P, g), we consider a linear connection preserving the almost product structure P and the Riemannian metric g and having a totally skew-symmetric torsion. We determine the class of the manifolds (M, P, g) admitting such a connection and prove that this connection is unique in terms of the covariant derivative of P with respect to the Levi-Civita connection. We find a necessary and sufficient condition the curvature tensor of the considered connection to have similar properties like the ones of the Kähler tensor in Hermitian geometry. We pay attention to the case when the torsion of the connection is parallel. We consider this connection on a Riemannian almost product manifold (G, P, g) constructed by a Lie group G.

scholarly journals On the geometry of affine Kähler immersions

1990 ◽  
Vol 120 ◽  
pp. 205-222 ◽  
Author(s):  
Katsumi Nomizu ◽  
Ulrich Pinkall ◽  
Fabio Podestà
Keyword(s):  
Isometric Immersion ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Complex Manifolds ◽  
Affine Immersion ◽  
Holomorphic Affine ◽  
Affine Immersions ◽  
Holomorphic Affine Immersion

In this paper we extend the work on affine immersions [N-Pi]-1 to the case of affine immersions between complex manifolds and lay the foundation for the geometry of affine Kähler immersions. The notion of affine Kähler immersion extends that of a holomorphic and isometric immersion between Kähler manifolds and can be contrasted to the notion of holomorphic affine immersion which has been established in the work of Dillen, Vrancken and Verstraelen [D-V-V] and that of Abe [A].

scholarly journals Codazzi and statistical connections on almost product manifolds

Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4343-4358
Author(s):  
E. Peyghan ◽  
C. Arcuş
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Product Manifold ◽  
Special Cases ◽  
Almost Product Manifold ◽  
Necessary And Sufficient

Considering an almost product manifold, we get the necessary and sufficient conditions for Codazzi connections on it. Also, we show that a Codazzi adapted connection on an almost product manifold, gives two type of Codazzi connections on it?s distributions, and moreover we study the conditions of holding the converse of this. Finally, we study the Codazzi (and statistical) structures for Schouten-Van Kampen and Vr?nceanu connections as two important special cases of adapted connections, and then we present some important examples of them.

scholarly journals Semi-invariant Riemannian submersions from nearly Kaehler manifolds

2020 ◽  
Vol 17 (07) ◽  
pp. 2050100
Author(s):  
Rupali Kaushal ◽  
Rashmi Sachdeva ◽  
Rakesh Kumar ◽  
Rakesh Kumar Nagaich
Keyword(s):  
Sufficient Conditions ◽  
Riemannian Submersion ◽  
Horizontal Distribution ◽  
Product Manifold ◽  
Riemannian Submersions ◽  
Kaehler Manifolds ◽  
Necessary And Sufficient ◽  
Nearly Kaehler Manifold ◽  
The Vertical Distribution ◽  
Usual Product

We study semi-invariant Riemannian submersions from a nearly Kaehler manifold to a Riemannian manifold. It is well known that the vertical distribution of a Riemannian submersion is always integrable therefore, we derive condition for the integrability of horizontal distribution of a semi-invariant Riemannian submersion and also investigate the geometry of the foliations. We discuss the existence and nonexistence of semi-invariant submersions such that the total manifold is a usual product manifold or a twisted product manifold. We establish necessary and sufficient conditions for a semi-invariant submersion to be a totally geodesic map. Finally, we study semi-invariant submersions with totally umbilical fibers.

Exit radii of submanifolds from cylindrical domains in warped product manifolds

2015 ◽  
Vol 145 (3) ◽  
pp. 559-569
Author(s):  
Hironori Kumura
Keyword(s):  
Lower Bound ◽  
Bounded Domain ◽  
Ricci Curvature ◽  
Mean Curvature ◽  
Warped Product ◽  
Product Manifold ◽  
Warped Product Manifold ◽  
Cylindrical Domains ◽  
The Mean

Let UB(p0; ρ1) × f MV be a cylindrically bounded domain in a warped product manifold := MB × fMV and let M be an isometrically immersed submanifold in . The purpose of this paper is to provide explicit radii of the geodesic balls of M which first exit from UB(p0; ρ1) × fMV for the case in which the mean curvature of M is sufficiently small and the lower bound of the Ricci curvature of M does not diverge to –∞ too rapidly at infinity.

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