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Hedgehogs are a natural generalization of convex bodies of class C+2. After recalling some basic facts concerning this generalization, we use the notion of index to study differential and integral geometries of hedgehogs.As applications, we prove a particular case of the Tennis Ball Theorem and a property of normals to a plane convex body of constant width.

Inequalities between the radii of spheres that are connected with a convex surface in a space of constant curvature.

Ionin, V.K. (2001)

Sibirskij Matematicheskij Zhurnal

Inequalities between volume, center of mass, circumscribed radius, order, and mean curvature.

Chen, Bang-yen, Jiang, Sheng (1995)

Bulletin of the Belgian Mathematical Society - Simon Stevin

Inequalities for radial Blaschke-Minkowski homomorphisms

Bo Wei, Weidong Wang, Fenghong Lu (2015)

Annales Polonici Mathematici

We establish $L_{p}$ Brunn-Minkowski type inequalities for radial Blaschke-Minkowski homomorphisms, which in special cases yield some new results for intersection bodies. Moreover, we obtain two monotonicity inequalities for radial Blaschke-Minkowski homomorphisms.

Inequalities of Willmore Type for Submanifolds.

U. Pinkall (1986)

Mathematische Zeitschrift

Infinite number of spheres through four tangents. (Unendlich viele Kugeln durch vier Tangenten.)

Stachel, Hellmuth (1995)

Mathematica Pannonica

Infinite periodic discrete minimal surfaces without self-intersections.

Rossman, Wayne (2005)

Balkan Journal of Geometry and its Applications (BJGA)

Infinitesimal automorphisms and deformations of parabolic geometries

Andreas Čap (2008)

Journal of the European Mathematical Society

We show that infinitesimal automorphisms and infinitesimal deformations of parabolic geometries can be nicely described in terms of the twisted de Rham sequence associated to a certain linear connection on the adjoint tractor bundle. For regular normal geometries, this description can be related to the underlying geometric structure using the machinery of BGG sequences. In the locally flat case, this leads to a deformation complex, which generalizes the well known complex for locally conformally...

Infinitesimal bending of a subspace of a space with non-symmetric basic tensor

Svetislav M. Minčić, Ljubica S. Velimirović (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this work infinitesimal bending of a subspace of a generalized Riemannian space (with non-symmetric basic tensor) are studied. Based on non-symmetry of the connection, it is possible to define four kinds of covariant derivative of a tensor. We have obtained derivation formulas of the infinitesimal bending field and integrability conditions of these formulas (equations).

Infinitesimal deformations and Lie derivative of a non-symmetric affine connection space

Ljubica S. Velimirović, Svetislav M. Minčić, Mića S. Stanković (2003)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Infinitesimal Deformations of Curvature Tensors at Non-symmetric Affine Connection Space

Ljubica S. Velimirović, Svetislav M. Minčić, Miomir Stanković (2002)

Matematički Vesnik

Infinitesimal rigidity of Euclidean submanifolds

M. Dajczer, L. L. Rodriguez (1990)

Annales de l'institut Fourier

A submanifold $M^{n}$ of the Euclidean space $R^{n}$ is said to be infinitesimally rigid if any smooth variation which is isometric to first order is trivial. The main purpose of this paper is to show that local or global conditions which are well known to imply isometric rigidity also imply infinitesimal rigidity.

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