Introduction to Differential Geometry

Introduction to Differential Geometry
Author: Joel W. Robbin
Publisher: Springer Nature
Total Pages: 426
Release: 2022-01-12
Genre: Mathematics
ISBN: 3662643405

This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point. The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor. An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.

Mathematical Reviews

Mathematical Reviews
Author: American Mathematical Society
Publisher: American Mathematical Society(RI)
Total Pages: 572
Release: 1981-12
Genre: Mathematics
ISBN:

The Relativistic Deduction

The Relativistic Deduction
Author: Émile Meyerson
Publisher: Springer Science & Business Media
Total Pages: 314
Release: 2012-12-06
Genre: Science
ISBN: 9400952112

When the author of Identity and Reality accepted Langevin's suggestion that Meyerson "identify the thought processes" of Einstein's relativity theory, he turned from his assured perspective as historian of the sciences to the risky bias of contemporary philosophical critic. But Emile Meyerson, the epis temologist as historian, could not find a more rigorous test of his conclusions from historical learning than the interpretation of Einstein's work, unless perhaps he were to turn from the classical revolution of Einstein's relativity to the non-classical quantum theory. Meyerson captures our sympathy in all his writings: " . . . the role of the epistemologist is . . . in following the development of science" (250); the study of the evolution of reason leads us to see that "man does not experience himself reasoning . . . which is carried on unconsciously," and as the summation of his empirical studies of the works and practices of scientists, "reason . . . behaves in an altogether predict able way: . . . first by making the consequent equivalent to the antecedent, and then by actually denying all diversity in space" (202). If logic - and to Meyerson the epistemologist is logician - is to understand reason, then "logic proceeds a posteriori. " And so we are faced with an empirically based Par menides, and, as we shall see, with an ineliminable 'irrational' within science. Meyerson's story, written in 1924, is still exciting, 60 years later.

The Shape of Inner Space

The Shape of Inner Space
Author: Shing-Tung Yau
Publisher: Il Saggiatore
Total Pages: 398
Release: 2010-09-07
Genre: Mathematics
ISBN: 0465020232

The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.

Biology, Medicine, and Surgery of Elephants

Biology, Medicine, and Surgery of Elephants
Author: Murray Fowler
Publisher: John Wiley & Sons
Total Pages: 597
Release: 2008-01-09
Genre: Medical
ISBN: 0470344113

Elephants are possibly the most well-known members of the animal kingdom. The enormous size, unusual anatomy, and longevity of elephants have fascinated humans for millenia. Biology, Medicine, and Surgery of Elephants serves as a comprehensive text on elephant medicine and surgery. Based on the expertise of 36 scientists and clinical veterinarians, this volume covers biology, husbandry, veterinary medicine and surgery of the elephant as known today. Written by the foremost experts in the field Comprehensively covers both Asian and African elephants Complete with taxonomy, behavioral, geographical and systemic information Well-illustrated and organized for easy reference