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Books on the topic 'Submanifolds theory'

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Published: 14 March 2023

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1

Takao, Akahori, and Nihon Sūgakkai, eds. CR-geometry and overdetermined systems. Tokyo, Japan: Published for the Mathematical Society of Japan by Kinokuniya Co., 1997.

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2

Palais, Richard S. Critical point theory and submanifold geometry. Berlin: Springer-Verlag, 1988.

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3

E, Chang Der-chen, ed. Sub-Riemannian geometry: General theory and examples. Cambridge: Cambridge University Press, 2009.

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4

Dajczer, Marcos, and Ruy Tojeiro. Submanifold Theory. New York, NY: Springer US, 2019. http://dx.doi.org/10.1007/978-1-4939-9644-5.

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5

Palais, Richard S., and Chuu-liang Terng. Critical Point Theory and Submanifold Geometry. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0087442.

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6

Li, Weiping, and Shihshu Walter Wei. Geometry and topology of submanifolds and currents: 2013 Midwest Geometry Conference, October 19, 2013, Oklahoma State University, Stillwater, Oklahoma : 2012 Midwest Geometry Conference, May 12-13, 2012, University of Oklahoma, Norman, Oklahoma. Providence, Rhode Island: American Mathematical Society, 2015.

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7

Georgia International Topology Conference (2009 University of Georgia). Low-dimensional and symplectic topology. Edited by Usher Michael 1978-. Providence, R.I: American Mathematical Society, 2011.

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8

(Dietmar), Salamon D., ed. J-holomorphic curves and symplectic topology. 2nd ed. Providence, R.I: American Mathematical Society, 2012.

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9

Ibragimov, Zair. Topics in several complex variables: First USA-Uzbekistan Conference on Analysis and Mathematical Physics, May 20-23, 2014, California State University, Fullerton, California. Providence, Rhode Island: American Mathematical Society, 2016.

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10

Southeast Geometry Seminar (15th 2009 University of Alabama at Birmingham). Geometric analysis, mathematical relativity, and nonlinear partial differential equations: Southeast Geometry Seminars Emory University, Georgia Institute of Technology, University of Alabama, Birmingham, and the University of Tennessee, 2009-2011. Edited by Ghomi Mohammad 1969-. Providence, Rhode Island: American Mathematical Society, 2013.

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11

Akahori, Takao. Cr-Geometry and over Determined Systems (Advanced Studies in Pure Mathematics). Amer Mathematical Society, 1997.

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12

Terng, Chuu-lian, and Richard S. Palais. Critical Point Theory and Submanifold Geometry. Springer, 1988.

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13

Terng, Chuu-lian, and Richard S. Palais. Critical Point Theory and Submanifold Geometry. Springer London, Limited, 2006.

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14

Calin, Ovidiu, and Der-Chen Chang. Sub-Riemannian Geometry: General Theory and Examples. Cambridge University Press, 2013.

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15

Calin, Ovidiu, and Der-Chen Chang. Sub-Riemannian Geometry: General Theory and Examples. Cambridge University Press, 2013.

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16

Calin, Ovidiu, and Der-Chen Chang. Sub-Riemannian Geometry: General Theory and Examples. Cambridge University Press, 2009.

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17

Dajczer, Marcos, and Ruy Tojeiro. Submanifold Theory: Beyond an Introduction. Springer, 2019.

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18

McDuff, Dusa, and Dietmar Salamon. The arnold conjecture. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198794899.003.0012.

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This chapter contains a proof of the Arnold conjecture for the standard torus, which is based on the discrete symplectic action. The symplectic part of this proof is very easy. However, for completeness of the exposition, one section is devoted to a fairly detailed discussion of the relevant Conley index theory and of Ljusternik–Schnirelmann theory. Closely related to the problem of finding symplectic fixed points is the Lagrangian intersection problem. The chapter outlines a proof of Arnold’s conjecture for cotangent bundles that again uses the discrete symplectic action, this time to construct generating functions for Lagrangian submanifolds. The chapter ends with a brief outline of the construction and applications of Floer homology.
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19

McDuff, Dusa, and Dietmar Salamon. Symplectic manifolds. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198794899.003.0004.

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The third chapter introduces the basic notions of symplectic topology, such as symplectic forms, symplectomorphisms, and Lagrangian submanifolds. A fundamental classical construction is Moser isotopy, with its various applications such as Darboux’s theorem and the Lagrangian neighbourhood theorem. The chapter now includes a brief discussion of the Chekanov torus and Luttinger surgery. The last section on contact structures has been significantly expanded.
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20

From Frenet to Cartan: The Method of Moving Frames. American Mathematical Society, 2017.

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21

Breadth in Contemporary Topology. American Mathematical Society, 2019.

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22

Mann, Peter. Constrained Lagrangian Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0008.

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This chapter builds on the previous two chapters to tackle constrained systems, using Lagrangian mechanics and constrained variations. The first section deals with holonomic constraint equations using Lagrange multipliers; these can be used to reduce the number of coordinates until a linearly independent minimal set is obtained that describes a constraint surface within configuration space, so that Lagrange equations can be set up and solved. Motion is understood to be confined to a constraint submanifold. The variational formulation of non-holonomic constraints is then discussed to derive the vakonomic formulation. These erroneous equations are then compared to the central Lagrange equation, and the precise nature of the variations used in each formulation is investigated. The vakonomic equations are then presented in their Suslov form (Suslov–vakonomic form) in an attempt to reconcile the two approaches. In addition, the structure of biological membranes is framed as a constrained optimisation problem.
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