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Title
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Geometry of submanifolds of all classes of third-order ODEs as a Riemannian manifold
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Type
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JournalPaper
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Keywords
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Levi-Civita connection, minimal surface, moving frame, Riemannian manifold, Riemann curvature tensor, totally geodesic
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Abstract
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In this paper, we prove that any surface corresponding to linear second-order ODEs as a submanifold is minimal in all classes of third-order ODEs y′′′ = f(x, y, p, q) as a Riemannian manifold where y′ = p and y′′ = q, if and only if qyy = 0. Moreover, we will see the linear second-order ODE with general form y′′ = ±y + β(x) is the only case that is defined a minimal surface and is also totally geodesic.
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Researchers
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Abolfazl Behzadi (Second Researcher), phatemah bakhshandeh (First Researcher), Mehdi Rafie-Rad (Fourth Researcher), Rohollah Bakhshandeh (Third Researcher)
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