Hyperbolic Riemann tensor

.zenodo.json

@@ -1,5 +1,11 @@
 {
         "contributors": [
+        {
+            "affiliation": "NTNU Trondheim",
+            "name": "Hajg Jasa",
+            "type": "ProjectMember",
+            "orcid": "0009-0002-7917-0530"
+        },
         {
             "name": "Mathieu Besançon",
             "type": "Other",

Project.toml

@@ -1,7 +1,7 @@
 name = "Manifolds"
 uuid = "1cead3c2-87b3-11e9-0ccd-23c62b72b94e"
 authors = ["Seth Axen <[email protected]>", "Mateusz Baran <[email protected]>", "Ronny Bergmann <[email protected]>", "Antoine Levitt <[email protected]>"]
-version = "0.8.76"
+version = "0.8.77"
 
 [deps]
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"

docs/src/references.bib

@@ -505,6 +505,14 @@ @article{LorenziPennec:2013
     TITLE      = {Efficient Parallel Transport of Deformations in Time Series of Images: From Schild's to Pole Ladder},
     JOURNAL    = {Journal of Mathematical Imaging and Vision}
 }
+@book{Lee:2019,
+    AUTHOR = {John M. Lee},
+    DOI    = {10.1007/978-3-319-91755-9},
+    ISBN = {978-3-319-91755-9},
+    PUBLISHER = {Springer Cham},
+    TITLE  = {Introduction to Riemannian Manifolds},
+    YEAR   = {2019}
+}
 #
 # M
 # ----------------------------------------------------------------------------------------
@@ -667,7 +675,7 @@ @book{SrivastavaKlassen:2016
     AUTHOR = {Anuj Srivastava and Eric P. Klassen},
     DOI    = {10.1007/978-1-4939-4020-2},
     ISBN = {978-1-4939-4018-9},
-    PUBLISHER = {Springer NEw York},
+    PUBLISHER = {Springer New York},
     TITLE  = {Functional and Shape Data Analysis},
     YEAR   = {2016}
 }

src/manifolds/Hyperbolic.jl

@@ -380,3 +380,22 @@ for (P, T) in zip(_ExtraHyperbolicPointTypes, _ExtraHyperbolicTangentTypes)
     @eval zero_vector(::Hyperbolic, p::$P) = $T(zero(p.value))
     @eval zero_vector!(::Hyperbolic, X::$T, ::$P) = fill!(X.value, 0)
 end
+
+@doc raw"""
+    riemann_tensor(M::Hyperbolic{n}, p, X, Y, Z)
+
+Compute the Riemann tensor ``R(X,Y)Z`` at point `p` on [`Hyperbolic`](@ref) `M`.
+The formula reads (see e.g., [Lee:2019](@cite) Proposition 8.36)
+
+````math
+R(X,Y)Z = - (\langle Z, Y \rangle X - \langle Z, X \rangle Y)
+````
+"""
+riemann_tensor(::Hyperbolic, p, X, Y, Z)
+
+function riemann_tensor!(M::Hyperbolic, Xresult, p, X, Y, Z)
+    innerZX = inner(M, p, Z, X)
+    innerZY = inner(M, p, Z, Y)
+    Xresult .= innerZX .* Y .- innerZY .* X
+    return Xresult
+end

test/manifolds/hyperbolic.jl

@@ -328,6 +328,26 @@ include("../utils.jl")
         A = change_metric(M, MinkowskiMetric(), p, X)
         @test A == X
     end
+    @testset "other metric" begin
+        M = Hyperbolic(2)
+        @test riemann_tensor(
+            M,
+            [0.0, 0.0, -1.0],
+            [-1.0, 0.0, 0.0],
+            [0.0, -1.0, 0.0],
+            [-0.5, -0.5, 0.0],
+        ) == [0.5, -0.5, 0.0]
+        X = [0.0, 0.0, 0.0]
+        @test riemann_tensor!(
+            M,
+            X,
+            [0.0, 0.0, -1.0],
+            [-1.0, 0.0, 0.0],
+            [0.0, -1.0, 0.0],
+            [-0.5, -0.5, 0.0],
+        ) === X
+        @test X == [0.5, -0.5, 0.0]
+    end
     @testset "ManifoldDiff" begin
         # ManifoldDiff
         M = Hyperbolic(2)