FragmentPagerAdapter Exists Only In Android.Support.V4.App (and not Android.App)

There is one that is in android.support.v13.app.FragmentPagerAdapter, which should do what you want it to do. It's a FragmentPagerAdapter for non-support fragments.

Android Studio Installation

Please add follow Gradle dependencies

dependencies {
    compile 'com.android.support:support-v13:+'
}

Ugh, you just need to use the FragmentPagerAdapter from the V13 support library

Android.Support.V13.App.FragmentPagerAdapter

Then all other Fragment related classes can be used from the "normal" libraries/namespaces, with the exception of ViewPager, but that's no big deal.

Here's a sample for completeness (modified "Support4" example from https://github.com/xamarin/monodroid-samples/):

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

using Android.App;
using Android.Content;
using Android.OS;
using Android.Runtime;
using Android.Util;
using Android.Views;
using Android.Widget;

using Java.Lang;

using Android.Support.V4.View;
using Fragment = Android.App.Fragment;

namespace Support4
{
    [Activity (Label = "@string/fragment_pager_support")]
    [IntentFilter (new[]{Intent.ActionMain}, Categories = new[]{ "mono.support4demo.sample" })]
    public class FragmentPagerSupport : Activity
    //public class FragmentPagerSupport : FragmentActivity
    {
        const int NUM_ITEMS = 4;

        protected MyAdapter _pagerAdapter;
        protected ViewPager _viewPager;

        protected override void OnCreate (Bundle bundle)
        {
            base.OnCreate (bundle);

            SetContentView(Resource.Layout.fragment_pager);

            List<Fragment> fragments = new List<Fragment>();

            // *** MonoDroid 4.2.7 letter case bug *** make's first letter lower.

            //string typeName = typeof(Fragment1).FullName;
            string typeName = "support4." + typeof(Fragment1).Name;

            fragments.Add(Fragment.Instantiate(this, typeName));
            fragments.Add(Fragment.Instantiate(this, typeName));
            fragments.Add(Fragment.Instantiate(this, typeName));
            fragments.Add(Fragment.Instantiate(this, typeName));

            //adapter = new MyAdapter(SupportFragmentManager);
            _pagerAdapter = new MyAdapter(FragmentManager, fragments);

            _viewPager = FindViewById<ViewPager>(Resource.Id.view_pager);
            _viewPager.Adapter = _pagerAdapter;
        }

        public override bool OnTouchEvent(MotionEvent e)
        {
            return base.OnTouchEvent(e);
        }

        protected class MyAdapter : Android.Support.V13.App.FragmentPagerAdapter
        {
            private List<Fragment> _fragments;

            public override Java.Lang.Object  InstantiateItem(View p0, int p1)
            {
                return base.InstantiateItem(p0, p1);
            }

            public MyAdapter(Android.App.FragmentManager fm)
                : base(fm)
            {

            }

            //public MyAdapter(Android.Support.V4.App.FragmentManager fm, List<Android.Support.V4.App.Fragment> fragments)
            //    : base(fm)
            public MyAdapter(FragmentManager fm, List<Fragment> fragments)
                : base(fm)
            {
                _fragments = fragments;
            }

            public override int Count {
                get {
                    return NUM_ITEMS;
                }
            }

            //public override Android.Support.V4.App.Fragment GetItem(int p0)
            public override Fragment GetItem(int p0)
            {
                return _fragments[p0];
            }

            public override float GetPageWidth(int p0)
            {
                //return base.GetPageWidth(p0);
                //base.GetPageWidth(p0);

                return (float)(0.5f);
            }
        }
    }

    //public class Fragment1 : Android.Support.V4.App.Fragment
    public class Fragment1 : Fragment
    {
        int num;

        private static int _colorIndex = 0;
        private static Android.Graphics.Color[] _colors = new[] { Android.Graphics.Color.Aqua, Android.Graphics.Color.DarkViolet,
        Android.Graphics.Color.Coral, Android.Graphics.Color.Bisque};

        public Fragment1()
        {
        }

        public Fragment1(int num)
        {
            var args = new Bundle();
            args.PutInt("num", num);
            Arguments = args;
        }

        public override void OnCreate(Bundle p0)
        {
            base.OnCreate(p0);

            num = Arguments != null ? Arguments.GetInt("num") : 1;
        }

        public override View OnCreateView(LayoutInflater inflater, ViewGroup container, Bundle savedInstanceState)
        {
            View v = inflater.Inflate(Resource.Layout.aaaaa, container, false);

            TextView tv = v.FindViewById<TextView>(Resource.Id.text);
            tv.Text = "# " + _colorIndex;
            tv.SetBackgroundColor(_colors[_colorIndex++]);

            return v;
        }

        public override void OnActivityCreated(Bundle p0)
        {
            base.OnActivityCreated(p0);
        }
    }
}

<?xml version="1.0" encoding="utf-8"?>
<!-- Copyright (C) 2010 The Android Open Source Project

     Licensed under the Apache License, Version 2.0 (the "License");
     you may not use this file except in compliance with the License.
     You may obtain a copy of the License at

          http://www.apache.org/licenses/LICENSE-2.0

     Unless required by applicable law or agreed to in writing, software
     distributed under the License is distributed on an "AS IS" BASIS,
     WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     See the License for the specific language governing permissions and
     limitations under the License.
-->

<!-- Top-level content view for the simple fragment sample. -->

<LinearLayout 
  xmlns:android="http://schemas.android.com/apk/res/android"
  android:orientation="horizontal" android:padding="4dip"
  android:layout_width="match_parent" android:layout_height="match_parent">
  <!--android:gravity="center_horizontal"-->

  <android.support.v4.view.ViewPager
    android:id="@+id/view_pager"
    android:layout_width="700dip"
    android:layout_height="match_parent"
    android:layout_weight="1"
    android:background="#FFCCFFFF">

    <!--android:layout_width="match_parent"-->
  </android.support.v4.view.ViewPager>

</LinearLayout>

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
    android:id="@+id/screen_container"
    android:orientation="horizontal"
    android:layout_width="match_parent"
    android:layout_height="match_parent">

  <TextView android:id="@+id/text"
      android:layout_width="match_parent" android:layout_height="match_parent"
      android:gravity="center_vertical|center_horizontal"
      android:textAppearance="?android:attr/textAppearanceMedium"
      android:text="@string/hello_world"
      android:background="#FF335555"/>

</LinearLayout>