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 Approximative K-atomic decompositions and frames in Banach spaces

2018 ◽  
Vol 26 (1/2) ◽  
pp. 153-166
Author(s):  
Shah Jahan
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Atomic Decomposition ◽  
Necessary Conditions ◽  
Bounded Operator ◽  
Special Kind ◽  
Frame Theory ◽  
Bessel Sequence ◽  
Atomic Decompositions ◽  
Counter Example

L. Gǎvruţa (2012) introduced a special kind of frames, named K-frames, where K is an operator, in Hilbert spaces, which is significant in frame theory and has many applications. In this paper, first of all, we have introduced the notion of approximative K-atomic decomposition in Banach spaces. We gave two characterizations regarding the existence of approximative K-atomic decompositions in Banach spaces. Also some results on the existence of approximative K-atomic decompositions are obtained. We discuss several methods to construct approximative K-atomic decomposition for Banach Spaces. Further, approximative d-frame and approximative d-Bessel sequence are introduced and studied. Two necessary conditions are given under which an approximative d-Bessel sequence and approximative d-frame give rise to a bounded operator with respect to which there is an approximative K-atomic decomposition. Example and counter example are provided to support our concept. Finally, a possible application is given.

scholarly journals Characterizations of Irregular Multigenerator Gabor Frame on Periodic Subsets of ℝ

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
D. H. Yuan ◽  
Y. Feng ◽  
Y. F. Shen ◽  
S. Z. Yang
Keyword(s):  
Necessary Conditions ◽  
Gabor Frame ◽  
Frame Theory ◽  
Parseval Frame

We consider the multigenerator system{EmblTnalφl,m,n∈ℤ,l=0,…,r-1}forφ0,…,φr-1∈L2(𝕊)anda0,b0,…,ar-1,br-1>0, where the parametersb0,…,br-1>0are not necessary the same. With the help of frame theory, we provide some sufficient or necessary conditions for the system to be a frame forL2(𝕊). Moreover, we present some characterizations for this system to be a Parseval frame.

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

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.

scholarly journals TightK-g-Frame and Its Novel Characterizations via Atomic Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Yongdong Huang ◽  
Dingli Hua
Keyword(s):  
Necessary Conditions ◽  
Frame Theory ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Atomic Systems ◽  
Methods And Techniques ◽  
Definition Of ◽  
Necessary And Sufficient

K-g-frame is a generalization ofg-frame. We generalize the tightg-frame toK-g-frame via atomic systems. In this paper, the definition of tightK-g-frame is put forward; equivalent characterizations and necessary conditions of tightK-g-frame are given. In particular, the necessary and sufficient condition for tightK-g-frame being tightg-frame is obtained. Finally, by means of methods and techniques of frame theory, several properties of tightK-g-frame are given.

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