Differential and Riemannian geometry

The book aims to present a comprehensive survey on biharmonic submanifolds and maps from the viewpoint of Riemannian geometry.

This volume contains papers by the main participants in the meeting of the 6th International Colloquium on Differential Geometry and its Related Fields (ICDG2018).

This book gathers contributions by respected experts on the theory of isometric immersions between Riemannian manifolds, and focuses on the geometry of CR structures on submanifolds in Hermitian manifolds.

A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature.

In this book we first review the ideas of Lie groupoid and Lie algebroid, and the associated concepts of connection.

The aim of the present book is to give a systematic treatment of the inverse problem of the calculus of variations, i.

The book is devoted to recent research in the global variational theory on smooth manifolds.

This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc.

The Hauptvermutung is the conjecture that any two triangulations of a poly- hedron are combinatorially equivalent.

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.

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.

Ordinary differential control thPory (the classical theory) studies input/output re- lations defined by systems of ordinary differential equations (ODE).

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

In this book the authors develop and work out applications to gravity and gauge theories and their interactions with generic matter fields, including spinors in full detail.

This book is about the light like (degenerate) geometry of submanifolds needed to fill a gap in the general theory of submanifolds.

One ofthe most important features of the development of physical and mathematical sciences in the beginning of the 20th century was the demolition of prevailing views of the three-dimensional Euclidean space as the only possible mathematical description of real physical space.

This monograph contains an exposition of the theory of minimal surfaces in Euclidean space, with an emphasis on complete minimal surfaces of finite total curvature.

Scale is a concept the antiquity of which can hardly be traced.

This is a monograph on geometrical and topological features which arise in quantum field theory.

This volume is based on the lectures given at the First Inter University Graduate School on Gravitation and Cosmology organized by IUCAA, Pune, in 1989.

Gauge theory, symplectic geometry and symplectic topology are important areas at the crossroads of several mathematical disciplines.

In the last decade several international conferences on Finsler, Lagrange and Hamilton geometries were organized in Braov, Romania (1994), Seattle, USA (1995), Edmonton, Canada (1998), besides the Seminars that periodically are held in Japan and Romania.

In this book we study sprays and Finsler metrics.

The theory of foliations and contact forms have experienced such great de- velopment recently that it is natural they have implications in the field of mechanics.

The development of dynamics theory began with the work of Isaac Newton.

This book contains an exposition of the theory of meromorphic functions and linear series on a compact Riemann surface.

Gaussian scale-space is one of the best understood multi-resolution techniques available to the computer vision and image analysis community.

The concept of ridges has appeared numerous times in the image processing liter- ature.

This book is an exposition of "e;Singular Semi-Riemannian Geometry"e;- the study of a smooth manifold furnished with a degenerate (singular) metric tensor of arbitrary signature.

The geometrical methods in modem mathematical physics and the developments in Geometry and Global Analysis motivated by physical problems are being intensively worked out in contemporary mathematics.

The present book has been written by two mathematicians and one physicist: a pure mathematician specializing in Finsler geometry (Makoto Matsumoto), one working in mathematical biology (Peter Antonelli), and a mathematical physicist specializing in information thermodynamics (Roman Ingarden).

This is a monograph on geometrical and topological features which arise in various quantization procedures.

Finslerian Laplacians have arisen from the demands of modelling the modern world.

This volume presents the lectures given during the second French-Uzbek Colloquium on Algebra and Operator Theory which took place in Tashkent in 1997, at the Mathematical Institute of the Uzbekistan Academy of Sciences.

In recent times it has been stated that many dynamical systems of classical mathematical physics and mechanics are endowed with symplectic structures, given in the majority of cases by Poisson brackets.

The erratic motion of pollen grains and other tiny particles suspended in liquid is known as Brownian motion, after its discoverer, Robert Brown, a botanist who worked in 1828, in London.

Advances in science and technology necessitate the use of increasingly-complicated dynamic control processes.

Geometric dynamics is a tool for developing a mathematical representation of real world phenomena, based on the notion of a field line described in two ways: -as the solution of any Cauchy problem associated to a first-order autonomous differential system; -as the solution of a certain Cauchy problem associated to a second-order conservative prolongation of the initial system.

The International Conference on Finsler and Lagrange Geometry and its Applications: A Meeting of Minds, took place August 13-20, 1998 at the University of Alberta in Edmonton, Canada.

This two-volume monograph obtains fundamental notions and results of the standard differential geometry of smooth (CINFINITY) manifolds, without using differential calculus.

During the last twenty-five years quite remarkable relations between nonas- sociative algebra and differential geometry have been discovered in our work.

Every group is represented in many ways as an epimorphic image of a free group.