On the covariant differential of an almost hermitian structure

1975 ◽  
Vol 50 (1) ◽  
pp. 137-143
Author(s):  
J. M. Terrier
Keyword(s):  
Hermitian Structure ◽  
Almost Hermitian Structure

scholarly journals Almost Hermitian structure on $S^6$

1955 ◽  
Vol 7 (3) ◽  
pp. 151-156 ◽  
Author(s):  
Tetsuzo Fukami ◽  
Shigeru Ishihara
Keyword(s):  
Hermitian Structure ◽  
Almost Hermitian Structure

CURVATURE AND INTEGRABILITY OF AN ALMOST HERMITIAN STRUCTURE

2006 ◽  
Vol 17 (01) ◽  
pp. 97-105 ◽  
Author(s):  
ZIZHOU TANG
Keyword(s):  
Necessary Conditions ◽  
Frame Theory ◽  
Hermitian Structure ◽  
Moving Frame ◽  
Almost Hermitian Structure

By using moving frame theory, we obtain some necessary conditions involving curvatures for integrability of an almost Hermitian structure. As consequences, they are applied to S6.

scholarly journals Twistorial construction of minimal hypersurfaces

2014 ◽  
Vol 11 (06) ◽  
pp. 1450064 ◽  
Author(s):  
Johann Davidov
Keyword(s):  
Twistor Space ◽  
Riemannian Metric ◽  
Hermitian Structure ◽  
Complex Structures ◽  
Minimal Hypersurfaces ◽  
Almost Hermitian Structure

Every almost Hermitian structure (g, J) on a four-manifold M determines a hypersurface ΣJ in the (positive) twistor space of (M, g) consisting of the complex structures anti-commuting with J. In this paper, we find the conditions under which ΣJ is minimal with respect to a natural Riemannian metric on the twistor space in the cases when J is integrable or symplectic. Several examples illustrating the obtained results are also discussed.

scholarly journals HARMONIC CONTACT METRIC STRUCTURES AND SUBMERSIONS

2009 ◽  
Vol 20 (02) ◽  
pp. 209-225 ◽  
Author(s):  
E. VERGARA-DIAZ ◽  
C. M. WOOD
Keyword(s):  
Hermitian Manifold ◽  
Hermitian Structure ◽  
Contact Structures ◽  
Warped Products ◽  
Almost Hermitian Manifold ◽  
Contact Metric Manifolds ◽  
Almost Hermitian Structure ◽  
Almost Contact Metric ◽  
Metric Structures

We study harmonic almost contact structures in the context of contact metric manifolds, and an analysis is carried out when such a manifold fibres over an almost Hermitian manifold, as exemplified by the Boothby–Wang fibration. Two types of almost contact metric warped products are also studied, relating their harmonicity to that of the almost Hermitian structure on the base or fibre.

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.

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