Displaying similar documents to “Affine surfaces with parallel shape operators”

Hypersurfaces with parallel affine curvature tensor R*

Barbara Opozda, Leopold Verstraelen (1999)

Annales Polonici Mathematici

Similarity:

In [OV] we introduced an affine curvature tensor R*. Using it we characterized some types of hypersurfaces in the affine space ℝ n + 1 . In this paper we study hypersurfaces for which R* is parallel relative to the induced connection.

Affine Independence in Vector Spaces

Karol Pąk (2010)

Formalized Mathematics

Similarity:

In this article we describe the notion of affinely independent subset of a real linear space. First we prove selected theorems concerning operations on linear combinations. Then we introduce affine independence and prove the equivalence of various definitions of this notion. We also introduce the notion of the affine hull, i.e. a subset generated by a set of vectors which is an intersection of all affine sets including the given set. Finally, we introduce and prove selected properties...

On the Cartan-Norden theorem for affine Kähler immersions

Maria Robaszewska (2000)

Annales Polonici Mathematici

Similarity:

In [O2] the Cartan-Norden theorem for real affine immersions was proved without the non-degeneracy assumption. A similar reasoning applies to the case of affine Kähler immersions with an anti-complex shape operator, which allows us to weaken the assumptions of the theorem given in [NP]. We need only require the immersion to have a non-vanishing type number everywhere on M.

Geometry of control-affine systems.

Clelland, Jeanne N., Moseley, Christopher G., Wilkens, George R. (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Similarity:

Mazur-Ulam Theorem

Artur Korniłowicz (2011)

Formalized Mathematics

Similarity:

The Mazur-Ulam theorem [15] has been formulated as two registrations: cluster bijective isometric -> midpoints-preserving Function of E, F; and cluster isometric midpoints-preserving -> Affine Function of E, F; A proof given by Jussi Väisälä [23] has been formalized.