Download Geometry and topology of submanifolds, IX : dedicated to by F Defever; J M Morvan; et al (eds.) PDF

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

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

Show description

Read 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

Similar geometry books

Handbook of the Geometry of Banach Spaces: Volume 1

The instruction manual offers an outline of such a lot points of recent Banach area conception and its purposes. The updated surveys, authored by way of top study employees within the sector, are written to be obtainable to a large viewers. as well as providing the cutting-edge of Banach house conception, the surveys talk about the relation of the topic with such components as harmonic research, advanced research, classical convexity, likelihood concept, operator conception, combinatorics, good judgment, geometric degree concept, and partial differential equations.

Geometry IV: Non-regular Riemannian Geometry

The ebook features a survey of study on non-regular Riemannian geome­ try out, performed commonly by means of Soviet authors. the start of this course oc­ curred within the works of A. D. Aleksandrov at the intrinsic geometry of convex surfaces. For an arbitrary floor F, as is understood, all these ideas that may be outlined and proof that may be tested by way of measuring the lengths of curves at the floor relate to intrinsic geometry.

Geometry Over Nonclosed Fields

According to the Simons Symposia held in 2015, the court cases during this quantity concentrate on rational curves on higher-dimensional algebraic kinds and purposes of the speculation of curves to mathematics difficulties. there was major development during this box with significant new effects, that have given new impetus to the examine of rational curves and areas of rational curves on K3 surfaces and their higher-dimensional generalizations.

Extra 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

Example text

Let x, x* be a polar pair and n = 3. Then the following statements are equivalent: (i) (M, I) is curvature homogeneous and H\ = constant; 42 (ii) (M, I*) is curvature homogeneous and H* = constant. 5. Corollary. Let x,x* : M -t S " + 1 ( l ) be polar hypersurfaces of dimension n > 3. Then the following statements are equivalent; (i) x is umbilical; (ii) x" is umbilical; (iii) (M, I) has constant sectional curvature; (iv) (M, f ) has constant sectional curvature. 6. Proposition. Let x, x" be polar.

1. Definition. Let (M, g) be a semi-Riemannian manifold and $ a Codazzi tensor. If the eigenvalues of $ are constant on M, $ is called an isoparametric Codazzi tensor. 2. Theorem. , en. ,n} befixed;then we have the Cartan identity J2 (Xi-\j)-lIC(ei,ej) =0 3 for g{ej,ek) = 6ik. 3. Corollary. Let x : M -> M(«) be a hypersurface in a space form M(K) of constant curvature K. ,fir. Then, for i € { 1 , . . 5. Weitzenboeck formulas. We recall two different versions of a Weitzenboeck for­ mula for traceless Codazzi tensors; see [WEG], [SI-1], [LIU-S-W]; [KOHL] contains other Weitzenboeck formulas.

3. Curvature relations b e t w e e n x and x'. ,n. For a polar pair x,x* : M -*• S " + 1 ( l ) we have: (i) The metric I is flat if and only if the polarized metric I* is flat; (ii) let 0 < r < n — 1 and r even; then H* is g-intrinsic (iii) let 0 < r < n - 1 and r odd; then {H*)2 is g-intrinsic and Hr is g*-intrinsic; and {Hr)2 is g'-intrinsic; (iv) if n=2 or 3

Download PDF sample

Rated 4.00 of 5 – based on 41 votes