Black-Box Optimization Using Geodesics in Statistical Manifolds by Jérémy Bensadon

“…Information geometric optimization (IGO) is a general framework for stochastic optimization problems aiming at limiting the influence of arbitrary parametrization choices: the initial problem is transformed into the optimization of a smooth function on a Riemannian manifold, defining a parametrization-invariant first order differential equation and, thus, yielding an approximately parametrization-invariant algorithm (up to second order in the step size). …”
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Fixed frequency eigenfunction immersions and supremum norms of random waves by Hanin, Boris, Canzani, Yaiza

“…A compact Riemannian manifold may be immersed into Euclidean space by using high frequency Laplace eigenfunctions. …”
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C[superscript ∞] Scaling Asymptotics for the Spectral Projector of the Laplacian by Canzani, Yaiza, Hanin, Boris

“…This article concerns new off-diagonal estimates on the remainder and its derivatives in the pointwise Weyl law on a compact n-dimensional Riemannian manifold. As an application, we prove that near any non-self-focal point, the scaling limit of the spectral projector of the Laplacian onto frequency windows of constant size is a normalized Bessel function depending only on n. …”
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Inverse spectral results for non-abelian group actions by Guillemin, Victor, Wang, Zuoqin

“…More precisely, Let G be a compact Lie group acting isometrically on a compact Riemannian manifold X. We will show that for the Schrödinger operator −ħ2Δ+V with V∈C∞(X)G, the potential function V is, in some interesting examples, determined by the G-equivariant spectrum. …”
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Constant Scalar Curvature Metrics on Connected Sums by Joyce, D

“…Let (M,g) be a compact Riemannian manifold with dimension n > 2. The Yamabe problem is to find a metric with constant scalar curvature in the conformal class of g, by minimizing the total scalar curvature. …”

The anelastic Ericksen's problem: universal eigenstrains and deformations in compressible isotropic elastic solids by Yavari, A, Goriely, A

“…We show that, in a simply-connected body, for any distribution of universal eigenstrains the material manifold is a symmetric Riemannian manifold and that in dimensions two and three the universal eigenstrains are zero-stress.…”

Isometric embedding via strongly symmetric positive systems by Chen, G, Clelland, J, Slemrod, M, Wang, D, Yang, D

“…We give a new proof for the local existence of a smooth isometric embedding of a smooth 3-dimensional Riemannian manifold with nonzero Riemannian curvature tensor into 6-dimensional Euclidean space. …”

Random Čech complexes on manifolds with boundary by de Kergorlay, H-L, Tillmann, U, Vipond, O

“…Let M be a compact, unit volume, Riemannian manifold with boundary. We study the homology of a random Čech-complex generated by a homogeneous Poisson process in M. …”

The anelastic Ericksen problem: universal deformations and universal eigenstrains in incompressible nonlinear anelasticity by Goodbrake, C, Yavari, A, Goriely, A

“…Second, we extend this problem to its anelastic version, where the stress-free configuration of the body is a Riemannian manifold. Physically, this situation corresponds to the case where nontrivial finite eigenstrains are present. …”

Neumann gradient estimate for nonlinear heat equation under integral Ricci curvature bounds by Hao-Yue Liu, Wei Zhang

“…<p>In this paper, we consider a Li-Yau gradient estimate on the positive solution to the following nonlinear parabolic equation</p> <p class="disp_formula">$ \frac{\partial}{\partial t}f = \Delta f+af(\ln f)^{p} $</p> <p>with Neumann boundary conditions on a compact Riemannian manifold satisfying the integral Ricci curvature assumption, where $ p\geq 0 $ is a real constant. …”
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Some notes on the tangent bundle with a Ricci quarter-symmetric metric connection by Yanlin Li, Aydin Gezer, Erkan Karakaş

“…Let $ (M, g) $ be an $ n $-dimensional (pseudo-)Riemannian manifold and $ TM $ be its tangent bundle $ TM $ equipped with the complete lift metric $ ^{C}g $. …”
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Killing and 2-Killing Vector Fields on Doubly Warped Products by Adara M. Blaga, Cihan Özgür

“…We provide a condition for a 2-Killing vector field on a compact Riemannian manifold to be Killing and apply the result to doubly warped product manifolds. …”
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On a Metric Affine Manifold with Several Orthogonal Complementary Distributions by Vladimir Rovenski, Sergey E. Stepanov

“…A Riemannian manifold endowed with <inline-formula><math display="inline"><semantics><mrow><mi>k</mi><mo>></mo><mn>2</mn></mrow></semantics></math></inline-formula> orthogonal complementary distributions (called here an almost multi-product structure) appears in such topics as multiply twisted or warped products and the webs or nets composed of orthogonal foliations. …”
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Multivariate time series classification using kernel matrix by Jiancheng Sun, Huimin Niu, Zongqing Tu, Zhinan Wu, Si Chen

“…Then the kernel matrix is mapped into the tangent space of Riemannian manifold. Finally, the classification is implemented by choosing a classification algorithm. …”
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Transversal Jacobi Operators in Almost Contact Manifolds by Jong Taek Cho, Makoto Kimura

“…Along a transversal geodesic <inline-formula><math display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> whose tangent belongs to the contact distribution <i>D</i>, we define the transversal Jacobi operator <inline-formula><math display="inline"><semantics><mrow><msub><mi>R</mi><mi>γ</mi></msub><mo>=</mo><mi>R</mi><mrow><mo>(</mo><mo>·</mo><mo>,</mo><mover accent="true"><mi>γ</mi><mo>˙</mo></mover><mo>)</mo></mrow><mover accent="true"><mi>γ</mi><mo>˙</mo></mover></mrow></semantics></math></inline-formula> on an almost contact Riemannian manifold <i>M</i>. Then, using the transversal Jacobi operator <inline-formula><math display="inline"><semantics><msub><mi>R</mi><mi>γ</mi></msub></semantics></math></inline-formula>, we give a new characterization of the Sasakian sphere. …”
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On the geometry of the tangent bundle with gradient Sasaki metric by Lakehal Belarbi, Hichem Elhendi

“…Purpose – Let (M, g) be a n-dimensional smooth Riemannian manifold. In the present paper, the authors introduce a new class of natural metrics denoted by gf and called gradient Sasaki metric on the tangent bundle TM. …”
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SEBARAN BAHANG DI PERMUKAAN BOLA DUA DIMENSI MELALUI PENDEKATAN KERNEL by , AL HARUN TAATE, S.Si, , Dr.rer.nat. Muh. Farchani Rosyid

“…Medium involved in our case here such as Riemannian manifold, that are the surface of a compact and uniform spherical. …”

Complex and Riemannian geometry: quaternionic manifolds by Salamon, S

“…</p> <p>The above theory is then applied to the case in which M is a Riemannian manifold with holonomy contained in Sp(n)Sp(l), using properties of Z to gain information about M. …”

Boundary rigidity of 3D CAT(0) cube complexes by Haslegrave, J, Scott, A, Tamitegama, Y, Tan, J

“…<p>The boundary rigidity problem is a classical question from Riemannian geometry: if (M, g) is a Riemannian manifold with smooth boundary, is the geometry of M determined up to isometry by the metric dg induced on the boundary &part;M? …”

An upper bound on the revised first Betti number and a torus stability result for RCD spaces by Mondello, I, Mondino, A, Perales, R

“…We prove an upper bound on the rank of the abelianised revised fundamental group (called "revised first Betti number") of a compact $RCD^{*}(K,N)$ space, in the same spirit of the celebrated Gromov-Gallot upper bound on the first Betti number for a smooth compact Riemannian manifold with Ricci curvature bounded below. …”