In this paper, we have defined recurrence and symmetry of different kinds in Hsu-structure manifold. Some theorem establishing relationship between recurrent H- HSU-Structure manifold involving equivalent conditions with respect to projective, conformal, conharmonic concircular curvature tensors has been discussed parameter also studied.

One hundred and ten children were studied 9 years after each had been in hospital for croup. They were evaluated with a questionnaire, physical examination, allergy skin testing, pulmonary function tests, and a histamine inhalation challenge. Fifty-seven of them had recurrent episodes of croup, and 33 were defined as allergic. The association between allergy and recurrent croup was highly signi...

Morse inequalities for diffeomorphisms of a compact manifold were first proved by Smale [21] under the assumption that the nonwandering set is finite. We call these the integral Morse inequalities. They were generalized by Zeeman in an unpublished work cited in [25] to diffeomorphisms with a hyperbolic chain recurrent set that is axiom-A-diffeomorphisms which satisfy the no cycle condition. For...

This paper investigates the appearance manifold of facial expression: embedding image sequences of facial expression from the high dimensional appearance feature space to a low dimensional manifold. We explore Locality Preserving Projections (LPP) to learn expression manifolds from two kinds of feature space: raw image data and Local Binary Patterns (LBP). For manifolds of different subjects, w...

We construct the twistor space associated with an HKT manifold, that is, a hyper-Kähler manifold with torsion, a type of geometry that arises as the target space geometry in two-dimensional sigma models with (4,0) supersymmetry. We show that this twistor space has a natural complex structure and is a holomorphic fibre bundle over the complex projective line with fibre the associated HKT manifol...