000 02242nam a22003618i 4500
001 CR9780511623783
003 UkCbUP
005 20200124160218.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 090916s1997||||enk o ||1 0|eng|d
020 _a9780511623783 (ebook)
020 _z9780521463003 (hardback)
020 _z9780521468312 (paperback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA649
_b.R68 1997
082 0 0 _a516.3/73
_220
100 1 _aRosenberg, Steven,
_d1951-
_eauthor.
245 1 4 _aThe Laplacian on a Riemannian manifold :
_ban introduction to analysis on manifolds /
_cSteven Rosenberg.
264 1 _aCambridge :
_bCambridge University Press,
_c1997.
300 _a1 online resource (x, 172 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aLondon Mathematical Society student texts ;
_v31
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
520 _aThis text on analysis of Riemannian manifolds is a thorough introduction to topics covered in advanced research monographs on Atiyah-Singer index theory. The main theme is the study of heat flow associated to the Laplacians on differential forms. This provides a unified treatment of Hodge theory and the supersymmetric proof of the Chern-Gauss-Bonnet theorem. In particular, there is a careful treatment of the heat kernel for the Laplacian on functions. The Atiyah-Singer index theorem and its applications are developed (without complete proofs) via the heat equation method. Zeta functions for Laplacians and analytic torsion are also treated, and the recently uncovered relation between index theory and analytic torsion is laid out. The text is aimed at students who have had a first course in differentiable manifolds, and the Riemannian geometry used is developed from the beginning. There are over 100 exercises with hints.
650 0 _aRiemannian manifolds.
650 0 _aLaplacian operator.
776 0 8 _iPrint version:
_z9780521463003
830 0 _aLondon Mathematical Society student texts ;
_v31.
856 4 0 _uhttps://doi.org/10.1017/CBO9780511623783
999 _c516482
_d516480