Araştırma Makalesi
BibTex RIS Kaynak Göster

On Four Dimensional Hermitian Manifolds

Yıl 2023, Cilt: 16 Sayı: 2, 697 - 706, 29.10.2023
https://doi.org/10.36890/iejg.1258996

Öz

The present paper is devoted to 4-dimentional Hermitain manifold. We give a new necessary and sufficient condition of integrability and we introduce a new class of locally conformal Kähler manifolds that we consider a twin of the Vaisman ones. Then, some basic properties of this class is discussed, also the existence of such manifolds is shown with concrete examples.

Teşekkür

It should be noted that this article is directed specifically to participate in the special issue of honoring the memory of the Prof. Dr. Krishan Lal Duggal.

Kaynakça

  • [1] Dragomir, S., Ornea, L.: Locally Conformal Kähler Geometry. Progress in Mathematics, vol. 55. Birkhäuser Boston, MA (1998). https://doi.org/10.1007/978-1-4612-2026-8
  • [2] Gray, A., Hervella, L. M.: The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura Appl. (4) 123, 35-58 (1980).
  • [3] Kenmotsu, K.: A class of almost contact Riemannian manifolds. Tohoku Math. J., 24, 93-103 (1972).
  • [4] Libermann, P.: Sur le problème d’équivalence de certaines structures infinitésimales régulières. Ann. Mat. Pura Appl. 36, 27-120 (1954). (InFrench.)
  • [5] Nagao, M., Kotô, S.: Curvature in almost Kähler spaces. Memoirs of The Faculty of Education. Niigata University (1973).
  • [6] Olszak, Z. : Curvature properties of four-dimentional Hermitian manifolds. Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 36, 169-179 (1987).
  • [7] Ornea, L., Verbitsky, M.: Structure theorem for compact Vaisman manifolds. Math. Res. Lett. 10, 799-805 (2003).
  • [8] Oubbich,e N., Beldjilali, G., Bouzir, H., Delloum, A.: New Class of Locally Conformal Kähler Manifolds. Mediterr. J. Math. (2023), doi.org/10.1007/s00009-023-02288-3
  • [9] Vaisman, I.: On locally conformal almost Kähler manifolds. Isr. J. Math. 24, 338-351 (1976).
  • [10] Yamaguchi, S.: On Kaehlerian torse-forming vector fields. Kodai Math. J. 2(1), 103-115 (1979).
  • [11] Yano, K.: On the torse-forming directions in Riemannian spaces. Proc. Imp. Acad. Tokyo. 20, 340-345 (1944).
  • [12] Yano, K., Kon, M.: Structures on Manifolds. Series in Pure Math., 3, World Sci., (1984).
Yıl 2023, Cilt: 16 Sayı: 2, 697 - 706, 29.10.2023
https://doi.org/10.36890/iejg.1258996

Öz

Kaynakça

  • [1] Dragomir, S., Ornea, L.: Locally Conformal Kähler Geometry. Progress in Mathematics, vol. 55. Birkhäuser Boston, MA (1998). https://doi.org/10.1007/978-1-4612-2026-8
  • [2] Gray, A., Hervella, L. M.: The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura Appl. (4) 123, 35-58 (1980).
  • [3] Kenmotsu, K.: A class of almost contact Riemannian manifolds. Tohoku Math. J., 24, 93-103 (1972).
  • [4] Libermann, P.: Sur le problème d’équivalence de certaines structures infinitésimales régulières. Ann. Mat. Pura Appl. 36, 27-120 (1954). (InFrench.)
  • [5] Nagao, M., Kotô, S.: Curvature in almost Kähler spaces. Memoirs of The Faculty of Education. Niigata University (1973).
  • [6] Olszak, Z. : Curvature properties of four-dimentional Hermitian manifolds. Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 36, 169-179 (1987).
  • [7] Ornea, L., Verbitsky, M.: Structure theorem for compact Vaisman manifolds. Math. Res. Lett. 10, 799-805 (2003).
  • [8] Oubbich,e N., Beldjilali, G., Bouzir, H., Delloum, A.: New Class of Locally Conformal Kähler Manifolds. Mediterr. J. Math. (2023), doi.org/10.1007/s00009-023-02288-3
  • [9] Vaisman, I.: On locally conformal almost Kähler manifolds. Isr. J. Math. 24, 338-351 (1976).
  • [10] Yamaguchi, S.: On Kaehlerian torse-forming vector fields. Kodai Math. J. 2(1), 103-115 (1979).
  • [11] Yano, K.: On the torse-forming directions in Riemannian spaces. Proc. Imp. Acad. Tokyo. 20, 340-345 (1944).
  • [12] Yano, K., Kon, M.: Structures on Manifolds. Series in Pure Math., 3, World Sci., (1984).
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Beldjilali Gherici 0000-0002-8933-1548

Erken Görünüm Tarihi 25 Ekim 2023
Yayımlanma Tarihi 29 Ekim 2023
Kabul Tarihi 7 Eylül 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 16 Sayı: 2

Kaynak Göster

APA Gherici, B. (2023). On Four Dimensional Hermitian Manifolds. International Electronic Journal of Geometry, 16(2), 697-706. https://doi.org/10.36890/iejg.1258996
AMA Gherici B. On Four Dimensional Hermitian Manifolds. Int. Electron. J. Geom. Ekim 2023;16(2):697-706. doi:10.36890/iejg.1258996
Chicago Gherici, Beldjilali. “On Four Dimensional Hermitian Manifolds”. International Electronic Journal of Geometry 16, sy. 2 (Ekim 2023): 697-706. https://doi.org/10.36890/iejg.1258996.
EndNote Gherici B (01 Ekim 2023) On Four Dimensional Hermitian Manifolds. International Electronic Journal of Geometry 16 2 697–706.
IEEE B. Gherici, “On Four Dimensional Hermitian Manifolds”, Int. Electron. J. Geom., c. 16, sy. 2, ss. 697–706, 2023, doi: 10.36890/iejg.1258996.
ISNAD Gherici, Beldjilali. “On Four Dimensional Hermitian Manifolds”. International Electronic Journal of Geometry 16/2 (Ekim 2023), 697-706. https://doi.org/10.36890/iejg.1258996.
JAMA Gherici B. On Four Dimensional Hermitian Manifolds. Int. Electron. J. Geom. 2023;16:697–706.
MLA Gherici, Beldjilali. “On Four Dimensional Hermitian Manifolds”. International Electronic Journal of Geometry, c. 16, sy. 2, 2023, ss. 697-06, doi:10.36890/iejg.1258996.
Vancouver Gherici B. On Four Dimensional Hermitian Manifolds. Int. Electron. J. Geom. 2023;16(2):697-706.