2017
DOI: 10.22436/jnsa.010.09.31
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Abstract: With a pair of conjugate connections ∇ and ∇ * , we derive optimal Casorati inequalities with the normalized scalar curvature on submanifolds of a statistical manifold of constant curvature.

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Cited by 16 publications
(17 citation statements)
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“…Several sharp inequalities between extrinsic and intrinsic curvatures for different submanifolds in real, complex, and quaternionic space forms endowed with various connections have been obtained (e.g., [14][15][16][17][18][19][20][21]). Such inequalities with a pair of conjugate affine connections involving the normalized scalar curvature of statistical submanifolds in different ambient spaces were obtained in [22][23][24][25][26].…”
Section: Introductionmentioning
confidence: 99%
“…Several sharp inequalities between extrinsic and intrinsic curvatures for different submanifolds in real, complex, and quaternionic space forms endowed with various connections have been obtained (e.g., [14][15][16][17][18][19][20][21]). Such inequalities with a pair of conjugate affine connections involving the normalized scalar curvature of statistical submanifolds in different ambient spaces were obtained in [22][23][24][25][26].…”
Section: Introductionmentioning
confidence: 99%
“…For the above problems, Aydin et al obtained Chen-Ricci inequalities [40] and a generalized Wintgen inequality [41] for submanifolds in statistical manifolds of constant curvature. Moreover, Lee et al established optimal inequalities involving the Casorati curvatures and the normalized scalar curvature on submanifolds of statistical manifolds of constant curvature [42]. These inequalities were extended by Aquib and Shahid [43] in the setting of statistical submanifolds in quaternion Kähler-like statistical space forms.…”
Section: Introductionmentioning
confidence: 99%
“…Some optimal inequalities involving Casorati curvatures were proved in [9][10][11][12][13][14][15] for several submanifolds in real, complex and quaternionic space forms with various connections. Moreover, Lee et al established that the normalized scalar curvature is bounded by Casorati curvatures of submanifolds in a statistical manifold of constant curvature [16]. In Kenmotsu statistical manifolds, Decu et al investigate curvature properties and establish optimizations in terms of a new extrinsic invariant (the normalized δ-Casorati curvature) and an intrinsic invariant (the scalar curvature) [17].…”
Section: Introductionmentioning
confidence: 99%