Araştırma Makalesi
Yıl 2024,
Cilt: 17 Sayı: 1, 199 - 206, 23.04.2024
Öz
We prove Maximal Diameter Theorems for pointed Riemannian manifolds which are compared to surfaces of revolution with weaker radial attraction.
Anahtar Kelimeler
Maximal diameter theorem maximal perimeter theorem weaker radial attraction
Kaynakça
- [1] Boonnam, N.: A generalized maximal diameter sphere theorem. Tohoku Math. J. 71 145-155 (2019).
- [2] Gluck H., Singer, D.: Scattering of geodesic fields II. Annals of Math. 110 205-225 (1979).
- [3] Hebda, J., Ikeda, Y.: Replacing the Lower Curvature Bound in Toponogov’s Comparison Theorem by a Weaker Hypothesis. Tohoku Math. J. 69 305-320 (2017).
- [4] Hebda, J., Ikeda, Y.: Necessary and Sufficient Conditions for a Triangle Comparison Theorem. Tohoku Math. J. 74 329-364 (2022).
- [5] Innami, N., K. Shiohama, K., Uneme, Y.: The Alexandrov–Toponogov Comparison Theorem for Radial Curvature. Nihonkai Math. J. 24 57-91 (2013).
- [6] Itokawa, Y., Machigashira, Y., Shiohama, K.:Generalized Toponogov’s Theorem for manifolds with radial curvature bounded below. Contemporary Mathematics. 332 121-130 (2003).
- [7] Shiohama, K., and Tanaka, M.: Compactification and maximal diameter theorem for noncompact manifolds with curvature bounded below. Mathematische Zeitschrift. 241 341-351 (2002).
- [8] Sinclair, R., Tanaka, M.: The cut locus of a sphere of revolution and Toponogov’s comparison theorem. Tohoku Math. J. 59 379-399 (2007).
- [9] Soga, T.: Remarks on the set of poles on a pointed complete surface. Nihonkai Math. J. 22 23-37 (2011).
- [10] Tanaka, M.: On a characterization of a surface of revolution with many poles. Mem. Fac. Sci. Kyushu Univ. Ser. A 46 251-268(1992).
Yıl 2024,
Cilt: 17 Sayı: 1, 199 - 206, 23.04.2024
Öz
Kaynakça
- [1] Boonnam, N.: A generalized maximal diameter sphere theorem. Tohoku Math. J. 71 145-155 (2019).
- [2] Gluck H., Singer, D.: Scattering of geodesic fields II. Annals of Math. 110 205-225 (1979).
- [3] Hebda, J., Ikeda, Y.: Replacing the Lower Curvature Bound in Toponogov’s Comparison Theorem by a Weaker Hypothesis. Tohoku Math. J. 69 305-320 (2017).
- [4] Hebda, J., Ikeda, Y.: Necessary and Sufficient Conditions for a Triangle Comparison Theorem. Tohoku Math. J. 74 329-364 (2022).
- [5] Innami, N., K. Shiohama, K., Uneme, Y.: The Alexandrov–Toponogov Comparison Theorem for Radial Curvature. Nihonkai Math. J. 24 57-91 (2013).
- [6] Itokawa, Y., Machigashira, Y., Shiohama, K.:Generalized Toponogov’s Theorem for manifolds with radial curvature bounded below. Contemporary Mathematics. 332 121-130 (2003).
- [7] Shiohama, K., and Tanaka, M.: Compactification and maximal diameter theorem for noncompact manifolds with curvature bounded below. Mathematische Zeitschrift. 241 341-351 (2002).
- [8] Sinclair, R., Tanaka, M.: The cut locus of a sphere of revolution and Toponogov’s comparison theorem. Tohoku Math. J. 59 379-399 (2007).
- [9] Soga, T.: Remarks on the set of poles on a pointed complete surface. Nihonkai Math. J. 22 23-37 (2011).
- [10] Tanaka, M.: On a characterization of a surface of revolution with many poles. Mem. Fac. Sci. Kyushu Univ. Ser. A 46 251-268(1992).
Toplam 10 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Cebirsel ve Diferansiyel Geometri |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Erken Görünüm Tarihi | 6 Nisan 2024 |
| Yayımlanma Tarihi | 23 Nisan 2024 |
| Gönderilme Tarihi | 1 Kasım 2023 |
| Kabul Tarihi | 5 Aralık 2023 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 17 Sayı: 1 |
