000 03637nam a22004335i 4500
001 978-1-4614-4244-8
003 DE-He213
005 20140220083249.0
007 cr nn 008mamaa
008 120731s2012 xxu| s |||| 0|eng d
020 _a9781461442448
_9978-1-4614-4244-8
024 7 _a10.1007/978-1-4614-4244-8
_2doi
050 4 _aQA641-670
072 7 _aPBMP
_2bicssc
072 7 _aMAT012030
_2bisacsh
082 0 4 _a516.36
_223
100 1 _aDeng, Shaoqiang.
_eauthor.
245 1 0 _aHomogeneous Finsler Spaces
_h[electronic resource] /
_cby Shaoqiang Deng.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2012.
300 _aXIV, 240 p. 1 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Monographs in Mathematics,
_x1439-7382
505 0 _aPreface -- Acknowledgements -- 1. Introduction to Finsler Geometry -- 2. Lie Groups and Homogenous Spaces -- 3. The Group of Isometries -- 4. Homogeneous Finsler Spaces -- 5. Symmetric Finsler Spaces -- 6. Weakly Symmetric Finsler Spaces -- 7. Homogeneous Randers Spaces -- References -- Index.  .
520 _aThis book is a unique addition to the existing literature in the field of Finsler geometry. This is the first monograph to deal exclusively with homogeneous Finsler geometry and to make serious use of Lie theory in the study of this rapidly developing field. The increasing activity in Finsler geometry can be attested in large part to the driving influence of S.S. Chern, its proven use in many fields of scientific study such as relativity, optics, geosciences, mathematical biology, and psychology, and its promising reach to real-world applications.  This work has potential for broad readership; it is a valuable resource not only for specialists of Finsler geometry, but also for differential geometers who are familiar with Lie theory, transformation groups, and homogeneous spaces. The exposition is rigorous, yet gently engages the reader—student and researcher alike—in developing a ground level understanding of the subject. A one-term graduate course in differential geometry and elementary topology are prerequisites. In order to enhance understanding, the author gives a detailed introduction and motivation for the topics of each chapter, as well as historical aspects of the subject, numerous well-selected examples, and thoroughly proved main results. Comments for potential further development are presented in Chapters 3–7.   A basic introduction to Finsler geometry is included in Chapter 1;  the essentials of the related classical theory of Lie groups, homogeneous spaces and groups of isometries are presented in Chapters 2–3. Then the author develops the theory of homogeneous spaces within the Finslerian framework. Chapters 4–6 deal with homogeneous, symmetric and weakly symmetric  Finsler spaces. Chapter 7  is entirely devoted to homogeneous Randers spaces,  which are good candidates for real world applications and beautiful illustrators of the developed theory.
650 0 _aMathematics.
650 0 _aGlobal differential geometry.
650 1 4 _aMathematics.
650 2 4 _aDifferential Geometry.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461442431
830 0 _aSpringer Monographs in Mathematics,
_x1439-7382
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-4244-8
912 _aZDB-2-SMA
999 _c101489
_d101489