This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, though their work, much of which has never appeared in book form before, can be extended to more general spaces. Many classical results are introduced and then extended by the authors. The compactification of complete open surfaces is discussed, as are Busemann functions for rays. Open problems are provided in each chapter, and the text is richly illustrated with figures designed to help the reader understand the subject matter and get intuitive ideas about the subject. The treatment is self-contained, assuming only a basic knowledge of manifold theory, so is suitable for graduate students and non-specialists who seek an introduction to this modern area of differential geometry.
This monograph studies the topological shapes of geodesics outside a large compact set in a finitely connected, complete, and noncompact surface admitting total curvature. When the surface is homeomorphic to a plane, all such geodesics behave like those of a flat cone. In particular, the rotation numbers of the geodesics are controlled by the total curvature. Accessible to beginners in differential geometry, but also of interest to specialists, this monograph features many illustrations that enhance understanding of the main ideas.
This volume is an English translation of Sakai's textbook on Riemannian Geometry which was originally written in Japanese and published in 1992. The author's intent behind the original book was to provide to advanced undergraduate and graudate students an introduction to modern Riemannian geometry that could also serve as a reference. The book begins with an explanation of the fundamental notion of Riemannian geometry. Special emphasis is placed on understandability and readability, to guide students who are new to this area. The remaining chapters deal with various topics in Riemannian geometry, with the main focus on comparison methods and their applications.
The Square Persimmon and Other Stories is an introduction to Takashi Atoda—one of Japan's most popular and versatile writers of fiction. Takashi Atocia is a master storyteller. Like the bar madam in "The Glow of Lipstick," he is capable of weaving a tale that captures the reader's attention from beginning to end. His plots deal with ordinary people, yet the emotional impact of each story is unusually strong. His down-to-earth characters inhabit a world that may at first appear familiar, but Atoda can so manipulate a scene that suddenly the reader is wondering whether it is reality or illusion that he is observing. Many stories feature bizarre endings. In these eleven stories, Atoda examines universal themes-first love, lost love, change, fate-through unmistakably Japanese eyes. The dreamlike quality of some stories invites the reader to draw his own conclusions in the denouement. Yet, in each one, Atoda brings to bear his precise style and his own unique vision, by turns mysterious, romantic, darkly humorous, and even bizarre.
Secret love is sweeter! The second volume of this popular yuri anthology goes dark, with stories about love between women that's hidden, unrequited, fantasy-based, or even taboo. Explore the forbidden side of love with new and returning artists in Volume 2 of Syrup.
This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, though their work, much of which has never appeared in book form before, can be extended to more general spaces. Many classical results are introduced and then extended by the authors. The compactification of complete open surfaces is discussed, as are Busemann functions for rays. Open problems are provided in each chapter, and the text is richly illustrated with figures designed to help the reader understand the subject matter and get intuitive ideas about the subject. The treatment is self-contained, assuming only a basic knowledge of manifold theory, so is suitable for graduate students and non-specialists who seek an introduction to this modern area of differential geometry.
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