A generalization of Baer’s theorem

In this paper, we studied the supersolvability of the product of two subgroups and got a generalization of Baer’s theorem.     

A generalization of Obata’s theorem

In a complete Riemannian manifold (M, g) if the hessian of a real-valued function satisfies some suitable conditions, then it restricts the geometry of (M, g). In this paper we characterize all compact rank-one symmetric spaces as those Riemannian manifolds (M, g) admitting a real-valued functionu such that the hessian ofu has at most two eigenvalues ?u and $ - \frac{{u + 1}}{2}$ under some mild hypotheses on (M, g). This generalizes a well-known result of Obata which characterizes all round spheres.     

A generalization of Jentzsch’s theorem

We study the asymptotic behavior of the roots of polynomials given by a linear summation method for partial sums of the Fourier series.     

A generalization of Forelli’s theorem

The purpose of this paper is to present a generalization of Forelli’s theorem. In particular, we prove an all dimensional version of the two-dimensional theorem of Chirka (Kompleks. Anal. i Prilozh, 232–240, 2006) of 2005.     

A generalization of Le Potier’s vanishing theorem

The main result is a general vanishing theorem for the cohomology of the ample vector bundles obtained as Schur functors of some vectors bundle which is not assumed to be ample itself. This is a generalization of Le Potiers vanishing theorem. It is also proven that for two partitions I and J such that IJ, the ampleness of S_IE implies that of S_JE.Mathematics Subject Classification (2000):14F17     

A generalization of a converse to Schur’s theorem

Niroomand (Arch. Math. 94 (2010) 401–404) proved a converse to a theorem of Schur in the following sense. He proved that if G is a group such that [G, G] is finite and G/Z(G) is finitely generated, then G/Z(G) is finite, of order bounded above by [G, G] ^k where k is the minimal number of generators required for G/Z(G). Here, we give a completely elementary short proof of a further generalization.     

A generalization of Bonnet’s theorem on Darboux surfaces

The well-known Bonnet theorem claims that, on a Darboux surface in three-dimensional Euclidean space, along each line of curvature, the corresponding principal curvature is proportional to the cube of another principal curvature. In the present paper, this theorem is generalized (with respect to dimension) to n-dimensional hypersurfaces of Euclidean spaces.     

A multidimensional generalization of Lagrange’s theorem on continued fractions

A multidimensional geometric analog of Lagrange’s theorem on continued fractions is proposed. The multidimensional generalization of the geometric interpretation of a continued fraction uses the notion of a Klein polyhedron, that is, the convex hull of the set of nonzero points in the lattice ? ⁿ contained inside some n-dimensional simplicial cone with vertex at the origin. A criterion for the semiperiodicity of the boundary of a Klein polyhedron is obtained, and a statement about the nonempty intersection of the boundaries of the Klein polyhedra corresponding to a given simplicial cone and to a certain modification of this cone is proved.     

A generalization of Fan��s matching theorem

We introduce a generalized coercivity type condition for setvalued maps defined on topological spaces endowed with a generalized convex structure and we extend Fan’s matching theorem.     

On Berndtsson’s generalization of Prékopa’s theorem

We present a new approach to Berndtssons complex extension of Prékopas theorem. This approach is inspired by the recent local proof of Prékopas theorem obtained by Ball, Barthe and Naor. In the complex setting, this approach leads to a formula expressing in terms of (derivatives of) where e^–(z)= As a consequence, we obtain new conditions ensuring that is subharmonic when is plurisubharmonic.