Lectures on Closed Geodesics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Closed Geodesics write by W. Klingenberg. This book was released on 2012-12-06. Lectures on Closed Geodesics available in PDF, EPUB and Kindle. The question of existence of c10sed geodesics on a Riemannian manifold and the properties of the corresponding periodic orbits in the geodesic flow has been the object of intensive investigations since the beginning of global differential geo metry during the last century. The simplest case occurs for c10sed surfaces of negative curvature. Here, the fundamental group is very large and, as shown by Hadamard [Had] in 1898, every non-null homotopic c10sed curve can be deformed into a c10sed curve having minimallength in its free homotopy c1ass. This minimal curve is, up to the parameterization, uniquely determined and represents a c10sed geodesic. The question of existence of a c10sed geodesic on a simply connected c10sed surface is much more difficult. As pointed out by Poincare [po 1] in 1905, this problem has much in common with the problem ofthe existence of periodic orbits in the restricted three body problem. Poincare [l.c.] outlined a proof that on an analytic convex surface which does not differ too much from the standard sphere there always exists at least one c10sed geodesic of elliptic type, i. e., the corres ponding periodic orbit in the geodesic flow is infinitesimally stable.
Lectures on Closed Geodesics
Lectures on Closed Geodesics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Closed Geodesics write by Wilhelm Klingenberg. This book was released on 1978. Lectures on Closed Geodesics available in PDF, EPUB and Kindle.
Lectures on Closed Geodesics
Lectures on Closed Geodesics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Closed Geodesics write by W Klingenberg. This book was released on 1978-01-01. Lectures on Closed Geodesics available in PDF, EPUB and Kindle.
Manifolds all of whose Geodesics are Closed
Manifolds all of whose Geodesics are Closed - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Manifolds all of whose Geodesics are Closed write by A. L. Besse. This book was released on 2012-12-06. Manifolds all of whose Geodesics are Closed available in PDF, EPUB and Kindle. X 1 O S R Cher lecteur, J'entre bien tard dans la sphere etroite des ecrivains au double alphabet, moi qui, il y a plus de quarante ans deja, avais accueilli sur mes terres un general epris de mathematiques. JI m'avait parle de ses projets grandioses en promettant d'ailleurs de m'envoyer ses ouvrages de geometrie. Je suis entiche de geometrie et c'est d'elle dontje voudrais vous parler, oh! certes pas de toute la geometrie, mais de celle que fait l'artisan qui taille, burine, amene, gauchit, peaufine les formes. Mon interet pour le probleme dont je veux vous entretenir ici, je le dois a un ami ebeniste. En effet comme je rendais un jour visite il cet ami, je le trouvai dans son atelier affaire a un tour. Il se retourna bientot, puis, rayonnant, me tendit une sorte de toupie et me dit: {laquo}Monsieur Besse, vous qui calculez les formes avec vos grimoires, que pensez-vous de ceci?)) Je le regardai interloque. Il poursuivit: {laquo}Regardez! Si vous prenez ce collier de laine et si vous le maintenez fermement avec un doigt place n'importe ou sur la toupie, eh bien! la toupie passera toujours juste en son interieur, sans laisser le moindre espace.)) Je rentrai chez moi, fort etonne, car sa toupie etait loin d'etre une boule. Je me mis alors au travail ...
