In this paper the symmetric differential and symmetric Lie derivative are introduced. Using these tools derivations of the algebra of symmetric tensors are classified. We also define a Frölicher-Nijenhuis bracket for vector valued symmetric tensors.
In this paper, under the one-parameter closed planar homothetic motion, a generalization of Holditch Theorem is obtained by using two different line segments (with fixed lengths) whose endpoints move along two different closed curves.
We estimate from below by geometric data the eigenvalues of the periodic Sturm-Liouville operator with potential given by the curvature of a closed curve.
A classical result of A. D. Alexandrov states that a connected compact smooth -dimensional manifold without boundary, embedded in , and such that its mean curvature is constant, is a sphere. Here we study the problem of symmetry of in a hyperplane in case satisfies: for any two points , on , with , the mean curvature at the first is not greater than that at the second. Symmetry need not always hold, but in this paper, we establish it under some additional condition for . Some variations...
A holomorphic representation formula for special parabolic hyperspheres is given.
We study the complex hypersurfaces which together with their transversal bundles have the property that around any point of M there exists a local section of the transversal bundle inducing a ∇-parallel anti-complex shape operator S. We give a class of examples of such hypersurfaces with an arbitrary rank of S from 1 to [n/2] and show that every such hypersurface with positive type number and S ≠ 0 is locally of this kind, modulo an affine isomorphism of .