Structure Sasakienne sur une variété Riemannienne
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Ce livre est destin� aux �tudiants de Master en g�om�trie diff�rentielle et applications, fili�re math�matiques et du domaine des math�matiques et de l'informatique. Il est r�dig� sous forme de cours d�taill�s, avec des exemples et des exercices r�solus, et il est pr�sent� dans un style tr�s simple qui permet aux �tudiants une compr�hension tr�s rapide. Ce cours, qui repr�sente une branche de la g�om�trie riemannienne, aborde ce que l'on appelle les structures compatibles sur une vari�t� riemannienne. La g�om�trie de contact entretient des liens �troits avec la g�om�trie symplectique, la g�om�trie complexe, la th�orie des feuilletages de codimension un et les syst�mes dynamiques. Elle est n�e de l'�tude de la thermodynamique et de l'optique g�om�trique. Ce travail se situe � l'interface de la g�om�trie riemannienne et de la g�om�trie de contact, exactement dans la g�om�trie sasakienne ou trans-sasakienne.Ces vari�t�s sasakiennes ont �t� introduites en 1960 par le g�om�tre Sasaki Shigeo. Il n'y a pas eu beaucoup d'activit�s dans ce domaine apr�s le milieu des ann�es 1970, jusqu'� l'av�nement de la th�orie des cordes (String Theory).
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