Keywords and phrases: curvature, curvature dual representation, integrals of curvature, curvature in Hilbert spaces, curvature in homogeneous spaces, smooth embedding, curvature integral transforms.
Received: March 2, 2021; Accepted: April 6, 2021; Published: April 27, 2021
How to cite this article: Francisco Bulnes, Dual representation of the curvature in a Hilbert space: curvature and integral transforms, JP Journal of Geometry and Topology 26(1) (2021), 39-51. DOI: 10.17654/GT026010039
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] F. Bulnes, Radon transform and curvature of a universe, Postgraduate Thesis, Facultad de Ciencias, UNAM, 2001. [2] F. Bulnes, Integral theory of the universe, Proc. Applied Math 2, IMUNAM, ESIME-IPN, Mexico City, 2006, pp. 73-122. [3] F. Bulnes, Research on Curvature of Homogeneous Spaces, TESCHA, Mexico, 2010, pp. 44-66. http://www.magnamatematica.org. [4] Helgason Sigurdur, Differential Geometry, Lie Groups and Symmetric Spaces, American Mathematical Society, USA, 1978. [5] Helgason Sigurdur, The Radon Transform, 2nd ed., Birkhäuser, 1999. [6] F. Bulnes, Detection of finite energy signals to the measurement of the universe curvature, Iberomet VII, Cancún, Quintana Roo, Mexico, 2002, pp. 825-843. [7] F. Bulnes, E. Hernandez and J. Maya, Design of measurement and detection devices of curvature through of the synergic integral operators of the mechanics on light waves, Proceedings of International Mechanics Engineering Conference and Exposition, Orlando Florida, 16 November 2009, pp. 91-102. doi:10.1115/IMECE2009-10038. [8] F. Bulnes, Extended d- cohomology and integral transforms in derived geometry to QFT-equations solutions using Langlands Correspondences, Theoretical Mathematics and Applications 7(2) (2017), 51-62. [9] Francisco Bulnes, Derived tensor products and their applications, Book Chapter of “Advances in Tensor Analysis and their Applications,” [Online First], IntechOpen, Intech, London, United Kingdom, June 25th 2020. DOI: 10.5772/intechopen.92869. Available from: https://www.intechopen.com/online-first/derived-tensorproducts-and-their-applications. [10] V. Voevodsky, Triangulated categories of motives over a field, Cycles, Transfers, and Motivic Homology Theories, Ann. of Math. Stud, Princeton University Press, USA, Vol. 143, 2000, pp. 188-238. [11] F. Bulnes, Integral Geometry Methods in the Geometrical Langlands Program, SCIRP, USA, 2016. [12] R. Donagi and T. Pantev, Lectures on the geometric Langlands conjecture and non-abelian Hodge theory, University of Pennsylvania, Department of Mathematics, Philadelphia, 2009. [13] F. Bulnes, Motivic hypercohomology solutions in field theory and applications in H-states, Journal of Mathematics Research 13(1) (2021), 31-40. [14] Francisco Bulnes, Detection and measurement of quantum gravity by a curvature energy sensor: H-states of curvature energy, Recent Studies in Perturbation Theory, Dimo Uzunov, ed., InTech, 2017. DOI: 10.5772/68026. [15] F. Bulnes, I. Martínez and O. Zamudio, Fine curvature measurements through curvature energy and their gauging and sensoring in the space, S. Y. Yurish, ed., Advances in Sensors Reviews 4, IFSA, Spain, 2016. [16] F. Bulnes, Y. Stropovsvky and I. Rabinovich, Curvature energy and their spectrum in the spinor-twistor framework: torsion as indicium of gravitational waves, Journal of Modern Physics 8 (2017), 1723-1736. doi: 10.4236/jmp.2017.810101.
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