By Elisabetta Barletta
ISBN-10: 0821843044
ISBN-13: 9780821843048
The authors research the connection among foliation conception and differential geometry and research on Cauchy-Riemann (CR) manifolds. the most items of research are transversally and tangentially CR foliations, Levi foliations of CR manifolds, strategies of the Yang-Mills equations, tangentially Monge-AmpГѓВ©re foliations, the transverse Beltrami equations, and CR orbifolds. the newness of the authors' strategy is composed within the total use of the tools of foliation thought and selection of particular functions. Examples of such functions are Rea's holomorphic extension of Levi foliations, Stanton's holomorphic degeneracy, Boas and Straube's nearly commuting vector fields process for the learn of worldwide regularity of Neumann operators and Bergman projections in multi-dimensional advanced research in different complicated variables, in addition to numerous purposes to differential geometry. Many open difficulties proposed within the monograph may possibly allure the mathematical group and bring about additional functions of foliation idea in advanced research and geometry of Cauchy-Riemann manifolds.
Read Online or Download Foliations in Cauchy-Riemann Geometry (Mathematical Surveys and Monographs) PDF
Similar geometry books
Challenges in Geometry: for Mathematical Olympians Past and - download pdf or read online
The identify of the e-book is a misnomer. This ebook infrequently offers with geometry, it is very a host thought ebook. while you're getting ready for the overseas arithmetic Olympiad (IMO) and desire to profit geometry, this isn't the ebook to check it from. whatever yet this ebook. this can be a quantity theroy publication i will be able to say.
Download PDF by A. V. Akopyan: Geometry of Conics
The e-book is dedicated to the homes of conics (plane curves of moment measure) that may be formulated and proved utilizing purely effortless geometry. beginning with the well known optical homes of conics, the authors flow to much less trivial effects, either classical and modern. specifically, the bankruptcy on projective homes of conics incorporates a distinct research of the polar correspondence, pencils of conics, and the Poncelet theorem.
Johannes de Tinemue's Redaction of Euclid's Elements, the - download pdf or read online
Euklids Hauptwerk, die Elemente, gilt als dasjenige wissenschaftliche Werk, das am häufigsten bearbeitet und benutzt wurde; es warfare ueber 2000 Jahre lang nicht nur das mathematische Lehrbuch schlechthin, sondern es beeinfluáte auch die Entwicklung anderer wissenschaftlicher Disziplinen. Das Werk wurde im 12.
Read e-book online Benoit Mandelbrot: A Life in Many Dimensions PDF
This can be a number of articles, many written by means of those who labored with Mandelbrot, memorializing the outstanding breadth and intensity of his paintings in technological know-how and the humanities. individuals contain mathematicians, physicists, biologists, economists, and engineers, as anticipated; and in addition artists, musicians, academics, an historian, an architect, a filmmaker, and a comic book.
Additional resources for Foliations in Cauchy-Riemann Geometry (Mathematical Surveys and Monographs)
Example text
25. 16) is direct. F. F) 9 T(C(M)) = Ker(a) ® Ker(d7r) 2. FOLIATED CR MANIFOLDS 30 then V = XT + fS for some X E T(M) and f E Coo(C(M)), where XT := 0 X. e. F)T + Ker(drr). 16) is proved. F). e. F). F). Then WH = 0. Since n _ 1 n+2{dy+rr`rlo } (for some 1-form rf on M, determined in terms of 9) and (dy)S = 1, it follows that rl(Wv) = 1/(n + 2). e. 19) G9((dir)VH, (dir)WH) + 9((d7r)WH)tl(Vv) = 0. Let us set W = V. e. (dir)VH = 0 hence Vii E Ker(drr) f1 Ker(q) = (0). F). e. Vv = 0. e. F). F) hence there F9 has signature (2n + 1 - q, 1).
Let F be a codimension q foliation of M. e. G9(X,T) = 0, X E T(M). e. do is a degenerate metric. We start by studying the geometry of F in (M, Go). The following concepts and terminology should be kept in mind as to degenerate metrics (cf. [97]). Let E --+ M be a real vector bundle of rank q (q > 2) over a C°° manifold M. 3A commutator of the form [X, YJ has length 2. 2. 7. By a (bundle) metric in E we intend a C°° section g : x E M - gx E Ey OR Ex* in E' ® E' such that gx is symmetric and has constant index ind(gx) = a, for any x E M.
The opposite inclusion may be proved in a similar manner. F)H(Af)]1) = (Y - 0(Y)T)1 = ao(HIY), for anyYET(M). 2. F) is degenerate in (T(M), G9). However, the pullback of F to the (total space of the) principal S'-bundle C(M) := [K(M) \ {zero section}]/IR+ turns out to be nondegenerate in (C(M), Fe), where Fe is the Fefferman metric of (M, 0). One may see C. M. Lee, [168], or the monograph [89] for a detailed description of the Fefferman metric. Nevertheless, to facilitate reading we collect a few notions and results below.
Foliations in Cauchy-Riemann Geometry (Mathematical Surveys and Monographs) by Elisabetta Barletta
by Joseph
4.1