TY  - JOUR
T1  - Generalized Ricci-Recurrent Weyl Manifolds
AU  - Arsan, Güler
AU  - Hafızoğlu Gökdağ, Zehra
PY  - 2024
DA  - October
Y2  - 2024
DO  - 10.36890/iejg.1360673
JF  - International Electronic Journal of Geometry
JO  - Int. Electron. J. Geom.
PB  - Kazım İlarslan
WT  - DergiPark
SN  - 1307-5624
SP  - 378
EP  - 387
VL  - 17
IS  - 2
LA  - en
AB  - This present paper is concerned with the study of the generalized Ricci-recurrent Weyl manifolds. First, we obtain a sufficient condition for the generalized Ricci-recurrent Weyl manifold admitting harmonic conformal curvature tensor to be a quasi-Einstein Weyl manifold. Also, we give an example of a quasi-Einstein Weyl manifold. Then, we prove that a generalized Ricci-recurrent Weyl manifold satisfying the Codazzi type of Ricci tensor is an Einstein Weyl manifold if and only if its scalar curvature is a prolonged covariant constant. Moreover, we prove that a generalized Ricci-recurrent Weyl manifold with a generalized concircularly symmetric tensor is an Einstein-Weyl manifold whose scalar curvature is prolonged covariant constant.
KW  - Generalized Ricci-recurrent Weyl manifold
KW  - quasi-Einstein Weyl manifold
KW  - harmonic conformal curvature tensor
KW  - Einstein Weyl manifold
KW  - concircular curvature tensor
CR  - [1] Arsan, G. G., Yildirim G. C.: Generalized circles and their conformal mapping in a subspace of a Weyl space. Acta Mathematica Scientia. 25 (2),
331-339 (2005).
CR  - [2] Canfes, E. Ö.: On generalizedrecurrent Weyl spaces and Wong’s conjecture, Differential Geometry and Dynamical Systems. 8, 34–42 (2006).
CR  - [3] Canfes, E. Ö, Özde˘ger, A.: Some applications of prolonged covariant differentiation in Weyl spaces, J.Geom. 60, 7–16 (1997).
CR  - [4] Chaki, M. C.: Some theorems on recurrent and Ricci-recurrent spaces, Rendiconti del Seminario Matematico della Università di Padova. 26,
168–176 (1956).
CR  - [5] Çivi, G., Arsan, G.G.: On Weyl manifolds with harmonic conformal curvature tensor, Analele Stiintifice ale Universitatii Al I Cuza din Iasi -
Matematica 1 (F2), 327–335 (2016).
CR  - [6] De, U. C., Guha, N., Kamilya, G.: On generalized Ricci-recurrent manifolds, Tensor N.S., 56, 312–317 (1995).
CR  - [7] Ghosh, A.: Einstein-Weyl Structure and Contact Geometry. Results Math 77, 58 (2022).
CR  - [8] Gül I., Canfes, E. Ö.: On quasi-Einstein Weyl manifolds, Int. J. Geom. Methods Mod. Phys. 14 (9), 1750–1822 (2017).
CR  - [9] Hlavaty, V.: Theorie d’immersion d’une Wm dans Wn, Ann. Soc. Polon. Math. 21, 196–206 (1949).
CR  - [10] Hitchin, N. J.: Complex Manifolds and Einstein Equations, in Twistor Geometry and Non-linear Systems (Primorsko, 1980), Lecture Notes
in Math. 970, Springer, Berlin - New York, 73—99 (1982).
CR  - [11] Honda, N., Nakata, F.: Minitwistor spaces, Severi varieties, and Einstein–Weyl structure. Ann Glob Anal Geom. 39, 293–323 (2011).
CR  - [12] Jones, P. E., Tod, K. P.: Minitwistor spaces and Einstein-Weyl spaces, Class. Quantum Grav. 2, 4, 565-577 (1985).
CR  - [13] Loo, T. H., De, A.: A classification of conformally flat generalized Ricci recurrent pseudo-Riemannian manifolds, Int. J. Geom. Methods Mod. Phys.
19(2), 2250023 (2022).
CR  - [14] Mallick, S., De, A., De, U. C.: On generalized Ricci recurrent manifolds with applications to relativity, Proceedings of the National Academy of
Sciences, India Section A: Physical Sciences, Springer, 143–152 (2013).
CR  - [15] Matsumoto, M.: On Riemannian spaces with recurrent projective curvature, Tensor N. S. 11–18 (1968).
CR  - [16] Miron, R.: Mouvements confermes dans les espaces Wn et Nn, Tensor N.S. 19, 33–41 (1968).
CR  - [17] Norden, A.: Affinely Connected Spaces. Moscow, Nauka, (in Russian) (1976).
CR  - [18] Özdeger, A., ¸Sentürk Z.: Generalized cirles in a Weyl space and their conformal mapping, Publ. Math. Debrecen 60(1-2), 75–87 (2002).
CR  - [19] Özdeger, A.: Conformal and generalized concircular mappings of Einstein-Weyl manifolds. Acta Math. Scientia Ser. B Engl. Ed. 30 (5), 1739–1745
(2010).
CR  - [20] Özdeger, A.: Generalized Einstein Tensor for a Weyl Manifold and Its Applications, Acta Math. Sinica, English Series Feb., 29 (2), 373—382
(2013).
CR  - [21] Patterson, E. M.: Some Theorems on Ricci-Recurrent Spaces, Journal of the London Mathematical Society 27 (3), 287–295 (1952).
CR  - [22] Prakash, N.: A note on Ricci-recurrent and recurrent spaces, Bull. Cal Math. Society 1–7 (1962).
CR  - [23] Pedersen, H., Tod, K. P.: Three-dimensional Einstein-Weyl Geometry, Adv. Math. 97, 74–109 (1993).
CR  - [24] Weyl, H.: Gravitation und Elektrizltdt, S.-B. Preuss. Akad. Wiss. Berlin, p. 465 (1918) (Translated in the principle of relativity, Dover
Books, New York).
CR  - [25] Yano, K.: Concircular geometry I. Concircular transformations. Proc. Imp. Acad. Tokyo 16, 195—200 (1940).
CR  - [26] Yılmaz, H. B.: On conformally symmetric generalized Ricci-recurrent manifolds with applications in general relativity, Bulletin of Mathematical
Analysis and Applications 13, 39–50 (2021).
CR  - [27] Zlatanov, G., Tsareva, B.: On the geometry of nets in the n-dimensional space of Weyl, J. Geom. 38 (1/2), 182–197 (1990).
UR  - https://doi.org/10.36890/iejg.1360673
L1  - https://dergipark.org.tr/en/download/article-file/3409530
ER  -