Research Article
PDF Zotero Mendeley EndNote BibTex Cite

Year 2021, Volume 14, Issue 1, 174 - 182, 15.04.2021
https://doi.org/10.36890/iejg.819887

Abstract

References

  • [1] Bazanfaré, M.: A volume comparison theorem and number of ends for manifolds with asymptotically nonnegative Ricci curvature. Revista Math. Compl. 13-2, 399–409 (2000).
  • [2] Galloway, G. J.: A generalization of Myers’ theorem and an application to relativistic cosmology. J. Differential Geom. 14-1, 105–116, (1979).
  • [3] Kaboye, I.A. and Bazanfaré, M.: Manifolds with Bakry-Émery Ricci Curvature Bounded Below. Advances in Pure Mathematics. 6, 754-764 (2016).
  • [4] Limoncu, M.: The Bakry-Émery Ricci tensor and its applications to some compactness theorems. Math. Z. 271, 715–722 (2012).
  • [5] Soylu, Y.: A Myers-type compactness theorem by the use of Bakry-Émery Ricci tensor. Differ. Geom. Appl. 54, 245–250 (2017).
  • [6] Tadano, H.: Some Ambrose and Galloway-type theorems via Bakry-Émery and modfied Ricci curvatures. Pacific J. Math. 294-1, 213-231 (2018).
  • [7] Wan, J.: An extension of Bonnet-Myers theorem. Math. Z. 291, 195–197 (2019).
  • [8] Wei, G. and Wylie, W.: Comparison geometry for the Bakry-Émery Ricci tensor. J. Differ. Geom. 83, 377–405 (2009).
  • [9] Wu, J.Y.: Myers’ type theorem with the Bakry-Émery Ricci tensor. Ann. Global Anal. Geom. 54-4, 541–549 (2018).

Some Myers-Type Theorems and Comparison Theorems for Manifolds with Modified Ricci Curvature

Year 2021, Volume 14, Issue 1, 174 - 182, 15.04.2021
https://doi.org/10.36890/iejg.819887

Abstract

 In this paper we establish some new compactness criteria for complete Riemannian manifolds with Bakry-\'Emery Ricci curvature bounded below. These results improve or generalize previous ones obtained by H. Tadano [6], J. Wan [7], I.A. Kaboye and M. Bazanfar\'e [3]. We also prove a volume comparison theorem for such manifolds.

References

  • [1] Bazanfaré, M.: A volume comparison theorem and number of ends for manifolds with asymptotically nonnegative Ricci curvature. Revista Math. Compl. 13-2, 399–409 (2000).
  • [2] Galloway, G. J.: A generalization of Myers’ theorem and an application to relativistic cosmology. J. Differential Geom. 14-1, 105–116, (1979).
  • [3] Kaboye, I.A. and Bazanfaré, M.: Manifolds with Bakry-Émery Ricci Curvature Bounded Below. Advances in Pure Mathematics. 6, 754-764 (2016).
  • [4] Limoncu, M.: The Bakry-Émery Ricci tensor and its applications to some compactness theorems. Math. Z. 271, 715–722 (2012).
  • [5] Soylu, Y.: A Myers-type compactness theorem by the use of Bakry-Émery Ricci tensor. Differ. Geom. Appl. 54, 245–250 (2017).
  • [6] Tadano, H.: Some Ambrose and Galloway-type theorems via Bakry-Émery and modfied Ricci curvatures. Pacific J. Math. 294-1, 213-231 (2018).
  • [7] Wan, J.: An extension of Bonnet-Myers theorem. Math. Z. 291, 195–197 (2019).
  • [8] Wei, G. and Wylie, W.: Comparison geometry for the Bakry-Émery Ricci tensor. J. Differ. Geom. 83, 377–405 (2009).
  • [9] Wu, J.Y.: Myers’ type theorem with the Bakry-Émery Ricci tensor. Ann. Global Anal. Geom. 54-4, 541–549 (2018).

Details

Primary Language English
Subjects Mathematics
Journal Section Research Article
Authors

Issa A. KABOYE This is me
Université de Zinder
Niger


Mahamane Mahi HAROUNA
Université Dan Dicko Dankoulodo de Maradi
Niger


Mahaman BAZANFARÉ (Primary Author)
Université Abdou Moumouni de Niamey
0000-0002-8085-2830
Niger

Publication Date April 15, 2021
Published in Issue Year 2021, Volume 14, Issue 1

Cite

Bibtex @research article { iejg819887, journal = {International Electronic Journal of Geometry}, issn = {}, eissn = {1307-5624}, address = {}, publisher = {Kazım İLARSLAN}, year = {2021}, volume = {14}, pages = {174 - 182}, doi = {10.36890/iejg.819887}, title = {Some Myers-Type Theorems and Comparison Theorems for Manifolds with Modified Ricci Curvature}, key = {cite}, author = {Kaboye, Issa A. and Harouna, Mahamane Mahi and Bazanfaré, Mahaman} }
APA Kaboye, I. A. , Harouna, M. M. & Bazanfaré, M. (2021). Some Myers-Type Theorems and Comparison Theorems for Manifolds with Modified Ricci Curvature . International Electronic Journal of Geometry , 14 (1) , 174-182 . DOI: 10.36890/iejg.819887
MLA Kaboye, I. A. , Harouna, M. M. , Bazanfaré, M. "Some Myers-Type Theorems and Comparison Theorems for Manifolds with Modified Ricci Curvature" . International Electronic Journal of Geometry 14 (2021 ): 174-182 <https://dergipark.org.tr/en/pub/iejg/issue/60718/819887>
Chicago Kaboye, I. A. , Harouna, M. M. , Bazanfaré, M. "Some Myers-Type Theorems and Comparison Theorems for Manifolds with Modified Ricci Curvature". International Electronic Journal of Geometry 14 (2021 ): 174-182
RIS TY - JOUR T1 - Some Myers-Type Theorems and Comparison Theorems for Manifolds with Modified Ricci Curvature AU - Issa A. Kaboye , Mahamane Mahi Harouna , Mahaman Bazanfaré Y1 - 2021 PY - 2021 N1 - doi: 10.36890/iejg.819887 DO - 10.36890/iejg.819887 T2 - International Electronic Journal of Geometry JF - Journal JO - JOR SP - 174 EP - 182 VL - 14 IS - 1 SN - -1307-5624 M3 - doi: 10.36890/iejg.819887 UR - https://doi.org/10.36890/iejg.819887 Y2 - 2021 ER -
EndNote %0 International Electronic Journal of Geometry Some Myers-Type Theorems and Comparison Theorems for Manifolds with Modified Ricci Curvature %A Issa A. Kaboye , Mahamane Mahi Harouna , Mahaman Bazanfaré %T Some Myers-Type Theorems and Comparison Theorems for Manifolds with Modified Ricci Curvature %D 2021 %J International Electronic Journal of Geometry %P -1307-5624 %V 14 %N 1 %R doi: 10.36890/iejg.819887 %U 10.36890/iejg.819887
ISNAD Kaboye, Issa A. , Harouna, Mahamane Mahi , Bazanfaré, Mahaman . "Some Myers-Type Theorems and Comparison Theorems for Manifolds with Modified Ricci Curvature". International Electronic Journal of Geometry 14 / 1 (April 2021): 174-182 . https://doi.org/10.36890/iejg.819887
AMA Kaboye I. A. , Harouna M. M. , Bazanfaré M. Some Myers-Type Theorems and Comparison Theorems for Manifolds with Modified Ricci Curvature. Int. Electron. J. Geom.. 2021; 14(1): 174-182.
Vancouver Kaboye I. A. , Harouna M. M. , Bazanfaré M. Some Myers-Type Theorems and Comparison Theorems for Manifolds with Modified Ricci Curvature. International Electronic Journal of Geometry. 2021; 14(1): 174-182.
IEEE I. A. Kaboye , M. M. Harouna and M. Bazanfaré , "Some Myers-Type Theorems and Comparison Theorems for Manifolds with Modified Ricci Curvature", International Electronic Journal of Geometry, vol. 14, no. 1, pp. 174-182, Apr. 2021, doi:10.36890/iejg.819887