Accession Number:

ADA207517

Title:

On a Computational Method for the Second Fundamental Tensor and Its Application to Bifurcation Problems.

Descriptive Note:

Technical rept.,

Corporate Author:

PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND APPLICATIONS

Report Date:

1989-02-01

Pagination or Media Count:

25.0

Abstract:

An algorithm is presented for the computation of the second fundamental tensor V of a Riemannian sub-manifold M of R superscript n. From V the Riemann curvature tensor of M is easily obtained. Moreover, V has a close relation to the second derivative of certain functionals on M which, in turn, provides a powerful new tool for the computational determination of multiple bifurcation directions. Frequently, in applications, the manifold M is defined implicitly as the zero set of a submersion F on R superscript n. In this case, the principal cost of algorithm for computing V p at a given point p an element of M involves only the decomposition of the Jacobian DF p of F at p and the projection of dd1 neighboring points onto M by means of a local iterative process using DFp. Several numerical examples are given which show the efficiency and dependability of the method. jhd

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE