A manifold is a Hausdorff topological space with some neighborhood of a point that looks like an open set in a Euclidean space. The concept of Euclidean space to a topological space is extended via suitable choice of coordinates. Manifolds are important objects in mathematics, physics and control theory, because they allow more complicated structures to be expressed and understood in terms of the well–understood properties of simpler Euclidean spaces. A differentiable manifold is defined either as a set of points with neighborhoods homeomorphic with Euclidean space, Rn with coordinates in overlapping neighborhoods being related by a differentiable transformation or as a subset of R, defined near each point by expressing some of the coordinates in terms of the others by differentiable functions. This paper aims at making a step by step introduction to differential manifolds.
| Published in | Mathematics Letters (Volume 2, Issue 5) |
| DOI | 10.11648/j.ml.20160205.11 |
| Page(s) | 32-35 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2016. Published by Science Publishing Group |
Submanifold, Differentiable Manifold, Morphism, Topological Space
| [1] | C. Lawrence, Differentiable Manifolds, 2nd Ed. Birkhauser advanced texts, Boston. ISBN-13: 978-0-8176-4767-4, 2001. |
| [2] | G. Pedro M., Masqué, J. Muñoz and M. Ihor, Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers, Second Edition. Springer London. ISBN 978-94-007-5952-7, 2013. |
| [3] | http://en.wikipedia.org/w/index.php?title=Differentiable_manifold&oldid=663213553 |
| [4] | Lang, Serge, Introduction to Differentiable Manifolds, 2nd ed. Springer-Verlag New York. ISBN 0-387-95477-5, 2002. |
| [5] | Lsham, Chris J., Modern Differential Geometry for Physicists, Second Edition. World Scientific Publishing Co. Re. Ltd., Singapore. ISBN 981-02-3562-3, 2001. |
| [6] | T. Fletcher, Terse Notes on Riemannian Geometry, January 2010. |
| [7] | http://en.wikipedia.org/wiki/Manifold |
| [8] | V. Ivancevic and T. Ivancevic, Applied Differential Geometry: A Modern Introduction World Scientific Publishing Co. Pte. Ltd, 2007 |
| [9] | T. Voronov, Differentiable Manifolds, Autumn, 2013. |
| [10] | S. Gudmundsson, Lecture Notes in Mathematics: An Introduction to Riemannian Geometry, Lund University, March 2016. |
| [11] | A. A. Kosinski, Differential Manifolds, Academic Press, Inc., San Diego, USA. ISBN 0-12-421850-4, 1993. |
APA Style
Kande Dickson Kinyua. (2016). An Introduction to Differentiable Manifolds. Mathematics Letters, 2(5), 32-35. https://doi.org/10.11648/j.ml.20160205.11
ACS Style
Kande Dickson Kinyua. An Introduction to Differentiable Manifolds. Math. Lett. 2016, 2(5), 32-35. doi: 10.11648/j.ml.20160205.11
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Download@article{10.11648/j.ml.20160205.11,
author = {Kande Dickson Kinyua},
title = {An Introduction to Differentiable Manifolds},
journal = {Mathematics Letters},
volume = {2},
number = {5},
pages = {32-35},
doi = {10.11648/j.ml.20160205.11},
url = {https://doi.org/10.11648/j.ml.20160205.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20160205.11},
abstract = {A manifold is a Hausdorff topological space with some neighborhood of a point that looks like an open set in a Euclidean space. The concept of Euclidean space to a topological space is extended via suitable choice of coordinates. Manifolds are important objects in mathematics, physics and control theory, because they allow more complicated structures to be expressed and understood in terms of the well–understood properties of simpler Euclidean spaces. A differentiable manifold is defined either as a set of points with neighborhoods homeomorphic with Euclidean space, Rn with coordinates in overlapping neighborhoods being related by a differentiable transformation or as a subset of R, defined near each point by expressing some of the coordinates in terms of the others by differentiable functions. This paper aims at making a step by step introduction to differential manifolds.},
year = {2016}
}
TY - JOUR T1 - An Introduction to Differentiable Manifolds AU - Kande Dickson Kinyua Y1 - 2016/11/23 PY - 2016 N1 - https://doi.org/10.11648/j.ml.20160205.11 DO - 10.11648/j.ml.20160205.11 T2 - Mathematics Letters JF - Mathematics Letters JO - Mathematics Letters SP - 32 EP - 35 PB - Science Publishing Group SN - 2575-5056 UR - https://doi.org/10.11648/j.ml.20160205.11 AB - A manifold is a Hausdorff topological space with some neighborhood of a point that looks like an open set in a Euclidean space. The concept of Euclidean space to a topological space is extended via suitable choice of coordinates. Manifolds are important objects in mathematics, physics and control theory, because they allow more complicated structures to be expressed and understood in terms of the well–understood properties of simpler Euclidean spaces. A differentiable manifold is defined either as a set of points with neighborhoods homeomorphic with Euclidean space, Rn with coordinates in overlapping neighborhoods being related by a differentiable transformation or as a subset of R, defined near each point by expressing some of the coordinates in terms of the others by differentiable functions. This paper aims at making a step by step introduction to differential manifolds. VL - 2 IS - 5 ER -
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