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Dergiler / International Electronic Journal of Geometry / 2018 / Cilt: 11 - Sayı: 2

A δ -Invariant for QR-Submanifolds in Quaternion Space Forms

Adela MIHAI
Gabriel MACSIM
Sayfa
8–17
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We obtain a relationship between intrinsicand extrinsic invariants for QR-submanifolds of quaternion space forms.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Starting from an inequality involving the invariant δ(D) for an anti-holomorphic submanifold ofa complex space form [1] and using optimization methods on Riemannian manifolds, we establisha corresponding inequality for the invariant δ(D ⊥ ) defined on QR-submanifolds in quaternionspace forms, in terms of the squared mean curvature.
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Temel Bulgular & Veri:Starting from an inequality involving the invariant δ(D) for an anti-holomorphic submanifold ofa complex space form [1] and using optimization methods on Riemannian manifolds, we establisha corresponding inequality for the invariant δ(D ⊥ ) defined on QR-submanifolds in quaternionspace forms, in terms of the squared mean curvature.
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Sonuç & Katkı:We obtain a relationship between intrinsicand extrinsic invariants for QR-submanifolds of quaternion space forms.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

Starting from an inequality involving the invariant δ(D) for an anti-holomorphic submanifold ofa complex space form [1] and using optimization methods on Riemannian manifolds, we establisha corresponding inequality for the invariant δ(D ⊥ ) defined on QR-submanifolds in quaternionspace forms, in terms of the squared mean curvature. We obtain a relationship between intrinsicand extrinsic invariants for QR-submanifolds of quaternion space forms.

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Bu Makaleye Atıf Yap

MIHAI, A., MACSIM, G. (2022). A δ -Invariant for QR-Submanifolds in Quaternion Space Forms. International Electronic Journal of Geometry, Cilt: 11 - Sayı: 2, 8–17. https://ajindex.com/articles/539667

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Kaynakça (6)

  1. Al-Solamy, F., Chen, B.-Y. and Deshmukh, S., Two optimal inequalities for anti-holomorphic submanifolds and their applications, Taiwanese J. Math. 18 (2014), no.1, 199-217.
  2. Bejancu, A., QR-submanifolds of quaternion Kaehler manifolds, Chinese J. Math. 14 (1986), no. 2, 81-94.
  3. Chen, B.-Y., CR-submanifolds of a Kaehler manifold, J. Diff. Geom. 16 (1981), 305-323.
  4. Chen, B.-Y., An optimal inequality for CR-warped products in complex space forms involving CR δ-invariant, Internat. J. Math. 23 (2012), no. 3, 1250045 (17 pages). Macsim, G. and Mihai, A., An inequality on quaternionic CR-submanifolds, Ann. Univ. Ovidius Constanţa, XXVI (2018), no. 3, to appear. Nash, J. F., The imbedding problem for Riemannian manifolds, Ann. of Math. 63 (1956), 20-63.
  5. Oprea, T., Optimizations on Riemannian submanifolds, Analele Univ. Buc. LIV 1 (2005), 127-136.
  6. Şahin, B., On QR-submanifolds of a quaternionic space forms, Turkish J. Math. 25 (2001), 413-425.