Differential and Riemannian geometry

The Yau-Tian-Donaldson conjecture for anti-canonical polarization was recently solved affirmatively by Chen-Donaldson-Sun and Tian.

This book, Differential Geometry: Riemannian Geometry and Isometric Immersions (Book I-B), is the second in a captivating series of four books presenting a choice of topics, among fundamental and more advanced in differential geometry (DG).

It is known that to any Riemannian manifold (M, g ) , with or without boundary, one can associate certain fundamental objects.

The falling cat is an interesting theme to pursue, in which geometry, mechanics, and control are in action together.

This book deals with the new class of one-dimensional variational problems - the problems with branching solutions.

This graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective.

The falling cat is an interesting theme to pursue, in which geometry, mechanics, and control are in action together.

This book provides the first-ever systematic introduction to the theory of Riemannian submersions, which was initiated by Barrett O'Neill and Alfred Gray less than four decades ago.

An important question in geometry and analysis is to know when two k-forms f and g are equivalent through a change of variables.

An exposition of the theory of curves over a finite field, and connections to the Riemann Hypothesis for function fields.

This text presents a graduate-level introduction to differential geometry for mathematics and physics students.

This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.

This textbook offers readers a self-contained introduction to quantitative Tamarkin category theory.

A major flaw in semi-Riemannian geometry is a shortage of suitable types of maps between semi-Riemannian manifolds that will compare their geometric properties.

The focus of this book is on providing students with insights into geometry that can help them understand deep learning from a unified perspective.

This contributed volume is the result of a July 2010 workshop at the University of Wuppertal Interdisciplinary Centre for Science and Technology Studies which brought together world-wide experts from physics, philosophy and history, in order to address a set of questions first posed in the 1950s: How do we compare spacetime theories?

This is the sixth volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research.

This book presents a multidisciplinary guide to gauge theory and gravity, with chapters by the world's leading theoretical physicists, mathematicians, historians and philosophers of science.

This introductory book offers a unique and unified overview of symplectic geometry, highlighting the differential properties of symplectic manifolds.

The subject of this volume, recent developments in foliation theory and important related analytic and geometric techniques, is an active field in the application of both global analysis and geometric topological theory of manifolds to the study of foliations.

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.

To our wives, Masha and Marian Interest in the so-called completely integrable systems with infinite num- ber of degrees of freedom was aroused immediately after publication of the famous series of papers by Gardner, Greene, Kruskal, Miura, and Zabusky [75, 77, 96, 18, 66, 19J (see also [76]) on striking properties of the Korteweg-de Vries (KdV) equation.

This book provides an introduction to geometric invariant theory from a differential geometric viewpoint.

Since the year 2000, we have witnessed several outstanding results in geometry that have solved long-standing problems such as the Poincare conjecture, the Yau-Tian-Donaldson conjecture, and the Willmore conjecture.

The book is devoted to algorithmic low-dimensional topology.

Written primarily for students who have completed the standard first courses in calculus and linear algebra, Elementary Differential Geometry, Revised 2nd Edition, provides an introduction to the geometry of curves and surfaces.

This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928 - February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics.

The theories of V.

This is a textbook on differential geometry well-suited to a variety of courses on this topic.

This textbook offers a different approach to classical textbooks in Differential Geometry.

This volume is a compilation of new results and surveys on the current state of some aspects of the foliation theory presented during the conference "e;FOLIATIONS 2012"e;.

This text presents a graduate-level introduction to differential geometry for mathematics and physics students.

In this monograph on twistor theory and its applications to harmonic map theory, a central theme is the interplay between the complex homogeneous geometry of flag manifolds and the real homogeneous geometry of symmetric spaces.

In this book, the optimal transportation problem (OT) is described as a variational problem for absolutely continuous stochastic processes with fixed initial and terminal distributions.

This monograph addresses two significant related questions in complex geometry: the construction of a Chern character on the Grothendieck group of coherent sheaves of a compact complex manifold with values in its Bott-Chern cohomology, and the proof of a corresponding Riemann-Roch-Grothendieck  theorem.

Differential forms satisfying the A-harmonic equations have found wide applications in fields such as general relativity, theory of elasticity, quasiconformal analysis, differential geometry, and nonlinear differential equations in domains on manifolds.

Wie bewegt sich ein Massenpunkt in einem Gebiet, an dessen Rand er elastisch zurückprallt?

This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Bedlewo, Poland in September 2015.

This book is about the smooth classification of a certainclass of algebraicsurfaces, namely regular ellipticsurfaces of geometric genus one, i.

This book contains an up-to-date survey and self-contained chapters on complex slant submanifolds and geometry, authored by internationally renowned researchers.

In these notes, we provide a summary of recent results on the cohomological properties of compact complex manifolds not endowed with a Kahler structure.