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A Course in Differential Geometry (Paperback, Softcover reprint of the original 1st ed. 1978): W. Klingenberg A Course in Differential Geometry (Paperback, Softcover reprint of the original 1st ed. 1978)
W. Klingenberg; Translated by D. Hoffman
R2,378 Discovery Miles 23 780 Ships in 18 - 22 working days

This English edition could serve as a text for a first year graduate course on differential geometry, as did for a long time the Chicago Notes of Chern mentioned in the Preface to the German Edition. Suitable references for ordin ary differential equations are Hurewicz, W. Lectures on ordinary differential equations. MIT Press, Cambridge, Mass., 1958, and for the topology of surfaces: Massey, Algebraic Topology, Springer-Verlag, New York, 1977. Upon David Hoffman fell the difficult task of transforming the tightly constructed German text into one which would mesh well with the more relaxed format of the Graduate Texts in Mathematics series. There are some e1aborations and several new figures have been added. I trust that the merits of the German edition have survived whereas at the same time the efforts of David helped to elucidate the general conception of the Course where we tried to put Geometry before Formalism without giving up mathematical rigour. 1 wish to thank David for his work and his enthusiasm during the whole period of our collaboration. At the same time I would like to commend the editors of Springer-Verlag for their patience and good advice. Bonn Wilhelm Klingenberg June,1977 vii From the Preface to the German Edition This book has its origins in a one-semester course in differential geometry which 1 have given many times at Gottingen, Mainz, and Bonn."

Lectures on Closed Geodesics (Paperback, Softcover reprint of the original 1st ed. 1978): W. Klingenberg Lectures on Closed Geodesics (Paperback, Softcover reprint of the original 1st ed. 1978)
W. Klingenberg
R2,866 Discovery Miles 28 660 Ships in 18 - 22 working days

The question of existence of c10sed geodesics on a Riemannian manifold and the properties of the corresponding periodic orbits in the geodesic flow has been the object of intensive investigations since the beginning of global differential geo metry during the last century. The simplest case occurs for c10sed surfaces of negative curvature. Here, the fundamental group is very large and, as shown by Hadamard [Had] in 1898, every non-null homotopic c10sed curve can be deformed into a c10sed curve having minimallength in its free homotopy c1ass. This minimal curve is, up to the parameterization, uniquely determined and represents a c10sed geodesic. The question of existence of a c10sed geodesic on a simply connected c10sed surface is much more difficult. As pointed out by Poincare [po 1] in 1905, this problem has much in common with the problem ofthe existence of periodic orbits in the restricted three body problem. Poincare [l.c.] outlined a proof that on an analytic convex surface which does not differ too much from the standard sphere there always exists at least one c10sed geodesic of elliptic type, i. e., the corres ponding periodic orbit in the geodesic flow is infinitesimally stable.

Riemannsche Hilbertmannigfaltigkeiten. Periodische Geodatische (German, Paperback, 1972 ed.): H. Karcher Riemannsche Hilbertmannigfaltigkeiten. Periodische Geodatische (German, Paperback, 1972 ed.)
H. Karcher; P. Flaschel, W. Klingenberg
R1,043 Discovery Miles 10 430 Ships in 18 - 22 working days
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