By F Defever; J M Morvan; et al (eds.)

ISBN-10: 9810238975

ISBN-13: 9789810238971

This quantity offers a scientific and unified method of the research, identity and optimum keep an eye on of continuous-time dynamical platforms through orthogonal polynomials (such as Legendre, Laguerre, Hermite, Tchebycheff, Jacobi and Gegenbauer) and through orthogonal features akin to sine-cosine, block-pulse, and Walsh. This ebook concentrates at the program of orthogonal polynomials in structures and keep watch over and goals to set up the prevalence of orthogonal polynomials over different orthogonal features

**Read Online or Download Geometry and topology of submanifolds, IX : dedicated to Prof. Radu Rosca on the ocasion of his 90th birthday, Valenciennes, France, 26-27 March, Lyon, France, 17-18 May, Leuven, Belgium, 19-20 September, 1997 PDF**

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**Additional info for Geometry and topology of submanifolds, IX : dedicated to Prof. Radu Rosca on the ocasion of his 90th birthday, Valenciennes, France, 26-27 March, Lyon, France, 17-18 May, Leuven, Belgium, 19-20 September, 1997**

**Sample text**

Z7 denotes the second fundamental form and S the Weingarten operator of x : M -> S n + 1 (l). Analogous notations yield for x* The following facts are obvious consequences of the structure equations. 3. Elementary facts. [0-2]. For a polar pair x,x* : M -> S n + 1 (l) we have (i) V is the Levi-Civita connection of the first fundamental form / of x, analogously V* of x*; (ii) the third fundamental forms 77/ of x and III* of x* satisfy III = /*, (iii) rankS = rankS* = n and S* = S _ 1 ; (iv) rank/7 = rank//* and // = //*.

I. OLIKER, U. SIMON*, C. P WANG ABSTRACT. We study pairs of polar hypersurfaces in spheres. Like for polar pairs of hypersur faces in Euclidean space we use a concept known from affine differential geometry, namely the notion of conjugate connections, as a basis for our investigation of polarization invariants. §1. Introduction. The duality principle is well known from classical projective geometry where the relation between sets of hyperplanes and their poles is studied quite thoroughly. g. [M], [0-1,2,3]).

I) We call <& a (Q,m)-Codazzi tensor (field) relative to V if the covariant derivative V<6 is totally symmetric. In this case we call {V, 3>} also a Codazzi pair. (ii) | f V is the Levi-Civita connection of a semi-Riemannian metric g we call $ also a (0, m)-Codazzi tensor relative to g. (iii) Similarly a (1,1)-tensor field $ is called a V-Codazzi operator if V\P is symmetric. (iv) If trace 9 $ = 0, we call $ traceless. The paper [LIU-S-W] lists references and examples. 2. Conjugate connections.

### Geometry and topology of submanifolds, IX : dedicated to Prof. Radu Rosca on the ocasion of his 90th birthday, Valenciennes, France, 26-27 March, Lyon, France, 17-18 May, Leuven, Belgium, 19-20 September, 1997 by F Defever; J M Morvan; et al (eds.)

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