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Relevant bibliographies by topics / Differentiable manifold

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Academic literature on the topic 'Differentiable manifold'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 April 2022

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Journal articles on the topic "Differentiable manifold"

1

Stepanov, S. E., I. I. Tsyganok, and V. Rovenski. "On conformal transformations of metrics of Riemannian paracomplex manifolds." Differential Geometry of Manifolds of Figures, no. 52 (2021): 117–22. http://dx.doi.org/10.5922/0321-4796-2020-52-11.

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A 2n-dimensional differentiable manifold M with -structure is a Riemannian almost paracomplex manifold. In the present paper, we consider conformal transformations of metrics of Riemannian paracomplex manifolds. In particular, a number of vanishing theorems for such transformations are proved using the Bochner technique.

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Velkoska, Aneta, and Zoran Misajleski. "Inner differentiability and differential forms on tangentially locally linearly independent sets." Filomat 34, no. 2 (2020): 365–72. http://dx.doi.org/10.2298/fil2002365v.

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The de Rham theorem gives a natural isomorphism between De Rham cohomology and singular cohomology on a paracompact differentiable manifold. We proved this theorem on a wider family of subsets of Euclidean space, on which we can define inner differentiability. Here we define this family of sets called tangentially locally linearly independent sets, propose inner differentiability on them, postulate usual properties of differentiable real functions and show that the integration over sets that are wider than manifolds is possible.

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CRESSON, JACKY. "NON-DIFFERENTIABLE DEFORMATIONS OF ℝn". International Journal of Geometric Methods in Modern Physics 03, № 07 (2006): 1395–415. http://dx.doi.org/10.1142/s0219887806001752.

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Many problems of physics or biology involve very irregular objects like the rugged surface of a malignant cell nucleus or the structure of space-time at the atomic scale. We define and study non-differentiable deformations of the classical Cartesian space ℝn which can be viewed as the basic bricks to construct irregular objects. They are obtained by taking the topological product of n-graphs of nowhere differentiable real valued functions. Our point of view is to replace the study of a non-differentiable function by the dynamical study of a one-parameter family of smooth regularization of this

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Fedorchuk, V. V. "A differentiable manifold with noncoinciding dimensions." Topology and its Applications 54, no. 1-3 (1993): 221–39. http://dx.doi.org/10.1016/0166-8641(93)90064-k.

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Fefferman, Charles, Sergei Ivanov, Yaroslav Kurylev, Matti Lassas, and Hariharan Narayanan. "Reconstruction and Interpolation of Manifolds. I: The Geometric Whitney Problem." Foundations of Computational Mathematics 20, no. 5 (2019): 1035–133. http://dx.doi.org/10.1007/s10208-019-09439-7.

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Abstract We study the geometric Whitney problem on how a Riemannian manifold (M, g) can be constructed to approximate a metric space $$(X,d_X)$$ ( X , d X ) . This problem is closely related to manifold interpolation (or manifold reconstruction) where a smooth n-dimensional submanifold $$S\subset {{\mathbb {R}}}^m$$ S ⊂ R m , $$m>n$$ m > n needs to be constructed to approximate a point cloud in $${{\mathbb {R}}}^m$$ R m . These questions are encountered in differential geometry, machine learning, and in many inverse problems encountered in applications. The determination of a Riemannian

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Lee, Manseob. "Positively Continuum-Wise Expansiveness for C1 Differentiable Maps." Mathematics 7, no. 10 (2019): 980. http://dx.doi.org/10.3390/math7100980.

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We show that if a differentiable map f of a compact smooth Riemannian manifold M is C 1 robustly positive continuum-wise expansive, then f is expanding. Moreover, C 1 -generically, if a differentiable map f of a compact smooth Riemannian manifold M is positively continuum-wise expansive, then f is expanding.

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BRANNLUND, JOHAN, ROBERT VAN DEN HOOGEN, and ALAN COLEY. "AVERAGING GEOMETRICAL OBJECTS ON A DIFFERENTIABLE MANIFOLD." International Journal of Modern Physics D 19, no. 12 (2010): 1915–23. http://dx.doi.org/10.1142/s0218271810018062.

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We construct a framework within which a mathematically precise, fully covariant, and exact averaging procedure for tensor fields on a manifold can be formulated. In particular, we introduce the Weitzenböck connection for parallel transport and argue that, within the context of averaging, frames and connections are the natural geometrical objects on the manifold.

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Smith, Patrick Adrian Neale. "Counterexamples to Smoothing Convex Functions." Canadian Mathematical Bulletin 29, no. 3 (1986): 308–13. http://dx.doi.org/10.4153/cmb-1986-047-5.

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AbstractGreene and Wu have shown that any continuous strongly convex function on a Riemannian manifold can be uniformly approximated by infinitely differentiable strongly convex functions. This result is not true if the word “strongly” is omitted; in this paper, we give examples of manifolds on which convex functions cannot be approximated by convex functions (k = 0, 1,2,...).

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Waliszewski, Wlodzimierz. "On differential spaces whose Cartesian product is a differentiable manifold." Colloquium Mathematicum 53, no. 2 (1987): 205–9. http://dx.doi.org/10.4064/cm-53-2-205-209.

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Vaisman, Izu. "Locally conformal symplectic manifolds." International Journal of Mathematics and Mathematical Sciences 8, no. 3 (1985): 521–36. http://dx.doi.org/10.1155/s0161171285000564.

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A locally conformal symplectic (l. c. s.) manifold is a pair(M2n,Ω)whereM2n(n>1)is a connected differentiable manifold, andΩa nondegenerate2-form onMsuch thatM=⋃αUα(Uα- open subsets).Ω/Uα=eσαΩα,σα:Uα→ℝ,dΩα=0. Equivalently,dΩ=ω∧Ωfor some closed1-formω. L. c. s. manifolds can be seen as generalized phase spaces of Hamiltonian dynamical systems since the form of the Hamilton equations is, in fact, preserved by homothetic canonical transformations. The paper discusses first Hamiltonian vector fields, and infinitesimal automorphisms (i. a.) on l. c. s. manifolds. If(M,Ω)has an i. a.Xsuch thatω(X

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Dissertations / Theses on the topic "Differentiable manifold"

1

Richardson, Peter A. (Peter Adolph) 1955. "Natural Smooth Measures on the Leaves of the Unstable Manifold of Open Billiard Dynamical Systems." Thesis, University of North Texas, 1998. https://digital.library.unt.edu/ark:/67531/metadc278917/.

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In this paper, we prove, for a certain class of open billiard dynamical systems, the existence of a family of smooth probability measures on the leaves of the dynamical system's unstable manifold. These measures describe the conditional asymptotic behavior of forward trajectories of the system. Furthermore, properties of these families are proven which are germane to the PYC programme for these systems. Strong sufficient conditions for the uniqueness of such families are given which depend upon geometric properties of the system's phase space. In particular, these results hold for a fairly no

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Ronchi, Elena. "The notion of curvature in differential geometry." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2021.

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In questo lavoro ci occupiamo di studiare la geometria differenziale delle superfici con un'attenzione particolare al concetto di curvatura. Nel primo capitolo studieremo le superfici, in particolare, immerse in spazi Euclidei utilizzando un approccio più semplice e concreto. Nel secondo capitolo introdurremo la nozione di forma differenziale e la applicheremo nello studio delle superfici all'interno degli spazi Euclidei attraverso il metodo dei moving frames. Presenteremo anche una generalizzazione del concetto di superficie, vale a dire ciò che chiameremo varietà differenziabile. Infine

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Kemp, M. C. "Geometric Seifert 4-manifolds with aspherical bases." University of Sydney. Mathematics, 2005. http://hdl.handle.net/2123/702.

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Seifert fibred 3-manifolds were originally defined and classified by Seifert. Scott gives a survey of results connected with these classical Seifert spaces, in particular he shows they correspond to 3-manifolds having one of six of the eight 3-dimensional geometries (in the sense of Thurston). Essentially, a classical Seifert manifold is a S1-bundle over a 2-orbifold. More generally, a Seifert manifold is the total space of a bundle over a 2-orbifold with flat fibres. It is natural to ask if these generalised Seifert manifolds describe geometries of higher dimension. Ue has considered the geom

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Kibildienė, Lina. "Specialių tiesinių elementų erdvių geometrija." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2009. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2009~D_20090629_132714-60483.

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Šiame darbe nagrinėjama speciali atraminių elementų erdvė – tiesinių elementų erdvė. Šios geometrijos bendrąją tiesinių ir afiniųjų siečių teoriją sukūrė V. Bliznikas. Jis parodė, [5] kaip tiesinės sieties geometrinis objektas indukuoja aukštesniųjų eilių afiniųjų, taip pat tenzorinių siečių objektams. V. Blizniko sukurtais tyrimo metodais dalinai naudojomės ir šiame darbe. Metrinių hiperplokštuminių elementų erdvė yra taip vadinamų normalizuotų erdvių atvejis. Normalizuotos erdvės tai tokios, kuriose apibrėžtos koks nors diferencialinis – geometrinis objektas, kurio invariantai ir sudaro norm

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Robinson, James Cooper. "Inertial manifolds." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.339420.

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Anderson, Laura Marie. "Topology of combinatorial differential manifolds." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/28093.

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Smith, John C. "The Computation of Ultrapowers by Supercompactness Measures." Thesis, University of North Texas, 1999. https://digital.library.unt.edu/ark:/67531/metadc2201/.

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The results from this dissertation are a computation of ultrapowers by supercompactness measures and concepts related to such measures. The second chapter gives an overview of the basic ideas required to carry out the computations. Included are preliminary ideas connected to measures, and the supercompactness measures. Order type results are also considered in this chapter. In chapter III we give an alternate characterization of 2 using the notion of iterated ordinal measures. Basic facts related to this characterization are also considered here. The remaining chapters are devoted to finding b

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Mong, Kai-Cheong. "Some differential invariants of 4-manifolds." Thesis, University of Oxford, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329918.

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Lee, Hwasung. "Strominger's system on non-Kähler hermitian manifolds." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:d3956c4f-c262-4bbf-8451-8dac35f6abef.

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In this thesis, we investigate the Strominger system on non-Kähler manifolds. We will present a natural generalization of the Strominger system for non-Kähler hermitian manifolds M with c₁(M) = 0. These manifolds are more general than balanced hermitian manifolds with holomorphically trivial canonical bundles. We will then consider explicit examples when M can be realized as a principal torus fibration over a Kähler surface S. We will solve the Strominger system on such construction which also includes manifolds of topology (k−1)(S²×S⁴)#k(S³×S³). We will investigate the anomaly cancellation co

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Schulze, Bert-Wolfgang. "Elliptic differential operators on manifolds with edges." Universität Potsdam, 2006. http://opus.kobv.de/ubp/volltexte/2009/3018/.

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On a manifold with edge we construct a specific class of (edgedegenerate) elliptic differential operators. The ellipticity refers to the principal symbolic structure σ = (σψ, σ^) of the edge calculus consisting of the interior and edge symbol, denoted by σψ and σ^, respectively. For our choice of weights the ellipticity will not require additional edge conditions of trace or potential type, and the operators will induce isomorphisms between the respective edge spaces.

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Books on the topic "Differentiable manifold"

1

Differential manifolds. Academic Press, 1993.

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Kosinski, Antoni A. Differential manifolds. Academic Press, 1992.

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Lang, Serge. Differential manifolds. Springer-Verlag, 1985.

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4

Conlon, Lawrence. Differentiable manifolds. 2nd ed. Birkhauser, 2001.

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Conlon, Lawrence. Differentiable Manifolds. Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-0-8176-4767-4.

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Torres del Castillo, Gerardo F. Differentiable Manifolds. Birkhäuser Boston, 2012. http://dx.doi.org/10.1007/978-0-8176-8271-2.

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Torres del Castillo, Gerardo F. Differentiable Manifolds. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45193-6.

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Conlon, Lawrence. Differentiable Manifolds. Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4757-2284-0.

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Differentiable manifolds. 2nd ed. Birkhäuser, 2001.

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Lang, Serge. Differential and Riemannian manifolds. Springer-Verlag, 1995.

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Book chapters on the topic "Differentiable manifold"

1

Cheng, Daizhan, Xiaoming Hu, and Tielong Shen. "Differentiable Manifold." In Analysis and Design of Nonlinear Control Systems. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11550-9_3.

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Itô, Kiyosi. "Stochastic Differential Equations in a Differentiable Manifold." In Selected Papers. Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4612-5370-9_8.

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Itô, Kiyosi. "Stochastic Differential Equations in a Differentiable Manifold (2)." In Selected Papers. Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4612-5370-9_13.

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Torres del Castillo, Gerardo F. "Manifolds." In Differentiable Manifolds. Birkhäuser Boston, 2012. http://dx.doi.org/10.1007/978-0-8176-8271-2_1.

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Torres del Castillo, Gerardo F. "Manifolds." In Differentiable Manifolds. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45193-6_1.

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6

Sinha, Rajnikant. "Differentiable Manifolds." In Smooth Manifolds. Springer India, 2014. http://dx.doi.org/10.1007/978-81-322-2104-3_1.

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Godinho, Leonor, and José Natário. "Differentiable Manifolds." In Universitext. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08666-8_1.

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Romano, Antonio, and Addolorata Marasco. "Differentiable Manifolds." In Classical Mechanics with Mathematica®. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-77595-1_6.

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Jänich, Klaus. "Differentiable Manifolds." In Vector Analysis. Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-3478-2_1.

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Berger, Marcel, and Bernard Gostiaux. "Differentiable Manifolds." In Graduate Texts in Mathematics. Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-1033-7_3.

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Conference papers on the topic "Differentiable manifold"

1

Luo, Shitong, and Wei Hu. "Differentiable Manifold Reconstruction for Point Cloud Denoising." In MM '20: The 28th ACM International Conference on Multimedia. ACM, 2020. http://dx.doi.org/10.1145/3394171.3413727.

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Sukthanker, Rhea Sanjay, Zhiwu Huang, Suryansh Kumar, Erik Goron Endsjo, Yan Wu, and Luc Van Gool. "Neural Architecture Search of SPD Manifold Networks." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/413.

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In this paper, we propose a new neural architecture search (NAS) problem of Symmetric Positive Definite (SPD) manifold networks, aiming to automate the design of SPD neural architectures. To address this problem, we first introduce a geometrically rich and diverse SPD neural architecture search space for an efficient SPD cell design. Further, we model our new NAS problem with a one-shot training process of a single supernet. Based on the supernet modeling, we exploit a differentiable NAS algorithm on our relaxed continuous search space for SPD neural architecture search. Statistical evaluation

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Son, Nguyen Thanh, Pierre-Yves Gousenbourger, Estelle Massart, and P. A. Absil. "Online balanced truncation for linear time-varying systems using continuously differentiable interpolation on Grassmann manifold." In 2019 6th International Conference on Control, Decision and Information Technologies (CoDIT). IEEE, 2019. http://dx.doi.org/10.1109/codit.2019.8820675.

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Natsiavas, Sotirios, Elias Paraskevopoulos, and Nikolaos Potosakis. "A New Theoretical and Numerical Approach to Finite Rigid Body Rotations Based on Lie Group Theory." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12426.

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A systematic theoretical approach is presented first, in an effort to provide a complete and illuminating study on motion of a rigid body rotating about a fixed point. Since the configuration space of this motion is a differentiable manifold possessing group properties, this approach is based on some fundamental concepts of differential geometry. A key idea is the introduction of a canonical connection, matching the manifold and group properties of the configuration space. Next, following the selection of an appropriate metric, the dynamics is also carried over. The present approach is theoret

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Colón, Diego. "Cartan’s Connection, Fiber Bundles and Quaternions in Kinematics and Dynamics Calculations." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46758.

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It is used the concept of Cartan’s connection and principal fiber bundles to obtain formulas for kinematics and dynamics calculations for robotic manipulators. A principal fiber bundle is a differentiable manifold formed by a base space B (in this case ℝ3)) plus all possible reference frames attached to a point p ∈ B (that is the fiber Sp). Cartan’s connections are the most general way to represent velocity of frames. In previous works, those ideas were applied to fiber bundles with fibers homomorphic to the Lie group SO(3) (or SE(3)). In this paper, it is applied to the case of fibers homomor

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Libermann, Paulette. "Charles Ehresmann's concepts in differential geometry." In Geometry and Topology of Manifolds. Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc76-0-2.

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OSINGA, HINKE, and REZA ROKNI. "NUMERICAL STUDY OF MANIFOLD COMPUTATIONS." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0020.

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Masa, Xosé, Enrique Macias-Virgós, and Jesús A. Alvarez López. "Analysis and Geometry in Foliated Manifolds." In 7th International Collóquium on Differential Geometry. WORLD SCIENTIFIC, 1996. http://dx.doi.org/10.1142/9789814533119.

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Paraskevopoulos, Elias, and Sotirios Natsiavas. "On a Consistent Application of Newton’s Law to Constrained Mechanical Systems." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12346.

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An investigation is carried out for deriving conditions on the correct application of Newton’s law of motion to mechanical systems subjected to constraints. It utilizes some fundamental concepts of differential geometry and treats both holonomic and anholonomic constraints. The focus is on establishment of conditions, so that the form of Newton’s law remains invariant when imposing an additional set of motion constraints on a system. Based on this requirement, two conditions are derived, specifying the metric and the form of the connection on the new manifold. The latter is weaker than a simil

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Liu, Xiyu, and Yinghong Ma. "Differential Evolutionary CLARANS on Manifold." In 2009 WRI World Congress on Computer Science and Information Engineering. IEEE, 2009. http://dx.doi.org/10.1109/csie.2009.11.

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Reports on the topic "Differentiable manifold"

1

Memoli, Facundo, Guillermo Sapiro, and Stanley Osher. Solving Variational Problems and Partial Differential Equations Mapping into General Target Manifolds. Defense Technical Information Center, 2002. http://dx.doi.org/10.21236/ada526351.

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