We establish some relative volume comparison theorems for extremal volume forms of‎ ‎Finsler manifolds under suitable curvature bounds‎. ‎As their applications‎, ‎we obtain some results on curvature and topology of Finsler manifolds‎. ‎Our results remove the usual assumption on S-curvature that is needed in the literature‎.

In this study the centre manifold is applied for reduction and limit cycle calculation of a highly nonlinear structural aeroelastic wing. The limit cycle is arisen from structural nonlinearity due to the large deflection of the wing. Results obtained by different orders of centre manifolds are compared with those obtained by time marching method (fourth-order Runge-Kutta method). These comparis...

This paper studies some properties of F-biharmonic maps between Riemannian manifolds. By considering the first variation formula of the F-bienergy functional, F-biharmonicity of conformal maps are investigated. Moreover, the second variation formula for F-biharmonic maps is obtained. As an application, instability and nonexistence theorems for F-biharmonic maps are given.

In this paper, we give a classification of non simply connected seven dimensional Reimannian manifolds of constant positive curvature which admit irreducible cohomogeneity-one actions. We characterize the acting groups and describe the orbits. The first and second homo-topy groups of the orbits have been presented as well.

‎In this paper we try to extend geometric concepts in the context of operator valued tensors‎. ‎To this end‎, ‎we aim to replace the field of scalars $ mathbb{R} $ by self-adjoint elements of a commutative $ C^star $-algebra‎, ‎and reach an appropriate generalization of geometrical concepts on manifolds‎. ‎First‎, ‎we put forward the concept of operator-valued tensors and extend semi-Riemannian...

This is a collection of notes on embedding problems for 3-manifolds. The main question explored is ‘which 3-manifolds embed smoothly in S4?’ The terrain of exploration is the Burton/Martelli/Matveev/Petronio census of triangulated prime closed 3-manifolds built from 11 or less tetrahedra. There are 13766 manifolds in the census, of which 13400 are orientable. Of the 13400 orientable manifolds, ...

we establish some relative volume comparison theorems for extremal volume forms of‎ ‎finsler manifolds under suitable curvature bounds‎. ‎as their applications‎, ‎we obtain some results on curvature and topology of finsler manifolds‎. ‎our results remove the usual assumption on s-curvature that is needed in the literature‎.

in this paper, we study projective randers change and c-conformal change of p-reduciblemetrics. then we show that every p-reducible generalized landsberg metric of dimension n  2 must be alandsberg metric. this implies that on randers manifolds the notions of generalized landsberg metric andberwald metric are equivalent.

‎In this paper‎, ‎we introduce the structure of a groupoid associated to a vector field‎ ‎on a smooth manifold‎. ‎We show that in the case of the $1$-dimensional manifolds‎, ‎our‎ ‎groupoid has a‎ ‎smooth structure such that makes it into a Lie groupoid‎. ‎Using this approach‎, ‎we associated to‎ ‎every vector field an equivalence‎ ‎relation on the Lie algebra of all vector fields on the smooth...

Almost hypercomplex manifolds with Norden metric are considered. A linear connection D is introduced such that the structure of these manifolds is parallel with respect to D. Of special interest is the class of the locally conformally equivalent manifolds to the hyper-Kähler manifolds with Norden metric and the case when the torsion of D is D-parallel. Curvature properties of these manifolds ar...