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

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

Adela MIHAI
Gabriel MACSIM
Pages
8–17
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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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Key Findings & Data: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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Conclusion & Impact:We obtain a relationship between intrinsicand extrinsic invariants for QR-submanifolds of quaternion space forms.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

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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Cite This Article

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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References (6)

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