scholarly journals Sasakian Hypersurfaces of the Generalized Concircular Recurrent Kahlerian Manifold

2008 ◽  
Vol 7 (2) ◽  
pp. 25-33
Author(s):  
Y. B. Maralabhavi ◽  
Hari Baskar R.
Keyword(s):  
Vector Fields ◽  
Sasakian Structure ◽  
Kählerian Manifold

In this paper we consider a recurrent sasakian hyper surface of the generalized con circular recurrent Kahlerian manifold and determine some conditions on the vector fields used in the sasakian structure. Further we determine such conditions for ϕ sasakian hyper surface also.

scholarly journals Skew-symmetric vector fields on aCR-submanifold of a para-Kählerian manifold

2004 ◽  
Vol 2004 (10) ◽  
pp. 535-540
Author(s):  
Adela Mihai ◽  
Radu Rosca
Keyword(s):  
Vector Field ◽  
Symplectic Form ◽  
Vector Fields ◽  
Geometric Properties ◽  
Infinitesimal Automorphism ◽  
Kählerian Manifold

We deal with aCR-submanifoldMof a para-Kählerian manifoldM˜, which carries aJ-skew-symmetric vector fieldX. It is shown thatXdefines a global Hamiltonian of the symplectic formΩonM⊤andJXis a relative infinitesimal automorphism ofΩ. Other geometric properties are given.

On six-dimensional AH-submanifolds of class W1⊕W2⊕W4 in Cayley algebra

2020 ◽  
pp. 7-13
Author(s):  
G. A. Banaru
Keyword(s):  
Structural Equations ◽  
Hermitian Structure ◽  
Sasakian Structure ◽  
Cayley Algebra ◽  
Almost Hermitian Structure ◽  
Locally Conformal ◽  
Kählerian Manifold ◽  
Vector Cross Products

Six-dimensional submanifolds of Cayley algebra equipped with an almost Hermitian structure of class W1 W2 W4 defined by means of three-fold vector cross products are considered. As it is known, the class W1 W2 W4 contains all Kählerian, nearly Kählerian, almost Kählerian, locally conformal Kählerian, quasi-Kählerian and Vaisman — Gray manifolds. The Cartan structural equations of the W1 W2 W4 -structure on such six-dimensional submanifolds of the octave algebra are obtained. A criterion in terms of the configuration tensor for an arbitrary almost Hermitian structure on a six-dimensional submanifold of Cayley algebra to belong to the W1 W2 W4 -class is established. It is proved that if a six-dimensional W1 W2 W4 -submanifold of Cayley algebra satisfies the quasi-Sasakian hypersurfaces axiom (i.e. a hypersurface with a quasi-Sasakian structure passes through every point of such submanifold), then it is an almost Kählerian manifold. It is also proved that a six-dimensional W1 W2 W4 -submanifold of Cayley algebra satisfies the eta-quasi-umbilical quasi-Sasakian hypersurfaces axiom, then it is a Kählerian manifold.

Parallel Computation of Complex Antennas around the Coated Object Using Iterative Vector Fields Technique

2014 ◽  
Vol E97.C (7) ◽  
pp. 661-669
Author(s):  
Ying YAN ◽  
Xunwang ZHAO ◽  
Yu ZHANG ◽  
Changhong LIANG ◽  
Zhewang MA
Keyword(s):  
Parallel Computation ◽  
Vector Fields

Spacetime symmetries

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Riemannian Manifold ◽  
Conservation Laws ◽  
Vector Fields ◽  
Killing Vector ◽  
Geodesic Equation ◽  
Spacetime Symmetries ◽  
Tensor Fields ◽  
Killing Vector Fields ◽  
Covariant Derivatives ◽  
Killing Equation

This chapter introduces tensor fields, covariant derivatives and the geodesic equation on a (pseudo-) Riemannian manifold. It discusses how symmetries of a general space-time can be found from the Killing equation, and how the existence of Killing vector fields is connected to global conservation laws.

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