<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$N^{2n+1}(\tilde{c})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>N</mi> <mrow> <mn>2</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo stretchy="false">(</mo> <mover accent="true"> <mi>c</mi> <mo stretchy="false">~</mo> </mover> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$n\ge 2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>) be the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$(2n+1)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-dimensional Sasakian space form with constant <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\varphi $</EquationSource> <EquationSource Format="MATHML"><math> <mi>φ</mi> </math></EquationSource> </InlineEquation>-sectional curvature <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\tilde{c}.$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mover accent="true"> <mi>c</mi> <mo stretchy="false">~</mo> </mover> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> In this paper, we study <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$(n+1)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-dimensional anti-invariant minimal submanifolds of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$N^{2n+1}(\tilde{c})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>N</mi> <mrow> <mn>2</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo stretchy="false">(</mo> <mover accent="true"> <mi>c</mi> <mo stretchy="false">~</mo> </mover> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> with constant sectional curvature <i>c</i>. As the main results, we first show that <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$c=0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>c</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$\tilde{c}\ge -3.$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mover accent="true"> <mi>c</mi> <mo stretchy="false">~</mo> </mover> <mo>≥</mo> <mo>-</mo> <mn>3</mn> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> Then we give a complete classification of such submanifolds.</p>

Anti-invariant minimal submanifolds of the Sasakian space forms with constant sectional curvature

期刊论文
发表日期：

2026年2月18日

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Xiuxiu Cheng,
Zejun Hu,
Cunjin Zong

摘要

Let $N^{2n+1}(\tilde{c})$ $N^{2 n + 1} (\tilde{c})$ ( $n\ge 2$ $n \geq 2$ ) be the $(2n+1)$ $(2 n + 1)$ -dimensional Sasakian space form with constant $\varphi $ $φ$ -sectional curvature $\tilde{c}.$ $\tilde{c} .$ In this paper, we study $(n+1)$ $(n + 1)$ -dimensional anti-invariant minimal submanifolds of $N^{2n+1}(\tilde{c})$ $N^{2 n + 1} (\tilde{c})$ with constant sectional curvature c. As the main results, we first show that $c=0$ $c = 0$ and $\tilde{c}\ge -3.$ $\tilde{c} \geq - 3 .$ Then we give a complete classification of such submanifolds.