Let (M, J, g) be an anti-Kähler manifold of dimension n = 2k with an almost complex structure J and a pseudo-Riemannian metric g and let T* M be its cotangent bundle with modified Riemannian extension metric <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\tilde{g}_{\nabla,G}$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <msub> <mrow> <mover> <mi>g</mi> <mo stretchy="false">~</mo> </mover> </mrow> <mrow> <mi mathvariant="normal">∇</mi> <mo>,</mo> <mi>G</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>. The modified Riemannian extension metric <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\tilde{g}_{\nabla,G}$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <msub> <mrow> <mover> <mi>g</mi> <mo stretchy="false">~</mo> </mover> </mrow> <mrow> <mi mathvariant="normal">∇</mi> <mo>,</mo> <mi>G</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> is obtained by deformation in the horizontal part of the Riemannian extension known in the literature by means of the twin Norden metric G. The paper aims first to examine the curvature properties of the cotangent bundle T* M with modified Riemannian extension metric <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\tilde{g}_{\nabla,G}$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <msub> <mrow> <mover> <mi>g</mi> <mo stretchy="false">~</mo> </mover> </mrow> <mrow> <mi mathvariant="normal">∇</mi> <mo>,</mo> <mi>G</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> and second to study some geometric solitons on the cotangent bundle T* M according to the modified Riemannian extension metric <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\tilde{g}_{\nabla,G}$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <msub> <mrow> <mover> <mi>g</mi> <mo stretchy="false">~</mo> </mover> </mrow> <mrow> <mi mathvariant="normal">∇</mi> <mo>,</mo> <mi>G</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>.

Some Soliton Structures on the Cotangent Bundle with Respect to the Modified Riemannian Extension

期刊论文
发表日期：

2025年11月1日

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Aydin Gezer,
Lokman Bilen

摘要

Let (M, J, g) be an anti-Kähler manifold of dimension n = 2k with an almost complex structure J and a pseudo-Riemannian metric g and let T* M be its cotangent bundle with modified Riemannian extension metric $\tilde{g}_{\nabla,G}$ ${\tilde{g}}_{\nabla, G}$ . The modified Riemannian extension metric $\tilde{g}_{\nabla,G}$ ${\tilde{g}}_{\nabla, G}$ is obtained by deformation in the horizontal part of the Riemannian extension known in the literature by means of the twin Norden metric G. The paper aims first to examine the curvature properties of the cotangent bundle T* M with modified Riemannian extension metric $\tilde{g}_{\nabla,G}$ ${\tilde{g}}_{\nabla, G}$ and second to study some geometric solitons on the cotangent bundle T* M according to the modified Riemannian extension metric $\tilde{g}_{\nabla,G}$ ${\tilde{g}}_{\nabla, G}$ .