Remarks on Cauchy-Riemann Structure
Main Article Content
Abstract
The present paper deals with Cauchy-Riemann structure (CR structure) satisfying relation \(F^{2\nu+3}+\lambda^rF^2=0\). Certain results with CR structure on distributions, mathematical operators, integrabitity condtions satisfying the above structure are established.
Article Details
References
- J. Nikic, Distribution’s Parallelism and Geodesics in the F(3; ε)-Structure Lagrangian Manifold, Novi Sad J. Math. 27 (1997), 117-125.
- H.M. Taston, M.D.Siddiqui, Anti-Invariant and Lagrangian Submersions From Trans-Sasakian Manifolds, Balkan J. Geom. Appl. 25 (2020), 106-123.
- R. Nivas, M. Saxena, On a Special Structure in a Differentiable Manifold, Demonstr. Math. 39 (2006), 203–210. https://doi.org/10.1515/dema-2006-0124.
- D. Demetropoulou-Psomopoulou. F.G. Andreou, On Necessary and Sufficient Conditions for an n-Dimensional Manifold to Admit a Tensor Field f(±0) of Type (1,1) Satisfying $f^{2nu+3}+f=0$, Tensor (N.S.), 42 (1985), 245-251. https://cir.nii.ac.jp/crid/1570854174724839680.
- R. Nivas, M. Saxena, On Complete and Horizontal Lifts From a Manifold with Hsu–(4,2) Structure to Its Cotangent Bundle, Nepali Math. Sci. Rep. 23 (2004), 35-42.
- M.N.I. Khan, F. Mofarreh, A. Haseeb, M. Saxena, Certain Results on the Lifts from an LP-Sasakian Manifold to Its Tangent Bundle Associated with a Quarter-Symmetric Metric Connection, Symmetry 15 (2023), 1553. https://doi.org/10.3390/sym15081553.
- M.N.I. Khan, L.S. Das, On CR-Structures and the General Quadratic Structure, J. Geom. Graph. 24 (2020), 249-255.
- M.N.I. Khan, Lifts of F(α, β)(3, 2, 1)-Structures From Manifolds to Tangent Bundles, Facta Univ. Ser. Math. Inform. 38 (2023), 209-218.
- M.N.I. Khan, Proposed Theorems for Lifts of the Extended Almost Complex Structures on the Complex Manifold, Asian-Eur. J. Math. 15 (2022), 2250200. https://doi.org/10.1142/S179355712250200X.
- M.N.I. Khan, M.A. Choudhary, S.K. Chaubey, Alternative Equations for Horizontal Lifts of the Metallic Structures from Manifold onto Tangent Bundle, J. Math. 2022 (2022), 5037620. https://doi.org/10.1155/2022/5037620.
- M.N.I. Khan, Integrability of the Metallic Structures on the Frame Bundle, Kyungpook Math. J. 61 (2021), 791–803. https://doi.org/10.5666/KMJ.2021.61.4.791.
- K. Yano, S. Ishihara, Tangent and Cotangent Bundles: Differential Geometry, Dekker, New York, 1973.
- D.E. Blair, B.-Y. Chen, On CR-Submanifolds of Hermitian Manifolds, Israel J. Math. 34 (1979), 353–363. https://doi.org/10.1007/BF02760614.
- L.S. Das, On CR-Structures and F(2K + 1, 1)-Structure Satisfying $F^{2K+1}+F=0$, J. Tensor Soc. India, 22 (2004), 1-7.
- L.S. Das, R. Nivas, M. Saxena, A Structure Defined by a Tensor Field of Type (1,1) Satisfying $(f^2+a^2)(f^2-a^2)(f^2+b^2)(f^2-b^2)=0$, Tensor N. S. 65 (2004), 36-41.
- M. Saxena, M.K. Manisha, R.A. Khan, Lifting of a Generalised Almost r-Contact Structure in a Tangent Bundle, Results Nonlinear Anal. 7 (2024), 194-201.
- S.B. Mishra, M. Saxena, P.K. Mathur, Aspects of Invariant Sub Manifold of a fλ-Hsu Manifold with Complemented Frames, J. Rajasthan Acad. Phys. Sci. 6 (2007), 179-188.
- J. Nikic, I. Comic, The Recurrent and Metric Connection andf-structures in Gauge Spaces of Second Order, Facta Univ. Ser. Mech. Autom. Control Robot. 5 (2006), 91-98.
- C. Miebach, K. Oeljeklaus, Compact Complex Non-Kähler Manifolds Associated with Totally Real Reciprocal Units, Math. Z. 301 (2022), 2747–2760. https://doi.org/10.1007/s00209-022-03010-x.
- H.M. Tastan, F. Ozdemir, C. Sayar, On Anti-Invariant Riemannian Submersions Whose Total Manifolds Are Locally Product Riemannian, J. Geom. 108 (2017), 411–422. https://doi.org/10.1007/s00022-016-0347-x.