Flutter TabView problem example

main.dart

import 'package:flutter/material.dart';

void main() => runApp(new MyApp());

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return new MaterialApp(
      title: 'Flutter Demo',
      theme: new ThemeData(
        primarySwatch: Colors.blue,
      ),
      home: new MyHomePage(),
    );
  }
}

class MyHomePage extends StatefulWidget {
  MyHomePage({Key key}) : super(key: key);

  @override
  _MyHomePageState createState() => new _MyHomePageState();
}

class _MyHomePageState extends State<MyHomePage> with SingleTickerProviderStateMixin {
  int _tabIndex = 0;
  List<Tab> _tabs = [
    Tab(text: 'Tab1'),
    Tab(text: 'Tab2'),
    Tab(text: 'Tab3')
  ];
  TabController _tabController;

  GlobalKey<FormState> _form1State = GlobalKey<FormState>();
  GlobalKey<FormState> _form2State = GlobalKey<FormState>();

  @override
  void initState() {
    _tabController = TabController(length: _tabs.length, vsync: this, initialIndex: _tabIndex);
    super.initState();
  }

  @override
  void dispose() {
    _tabController.dispose();
    super.dispose();
  }

  @override
  Widget build(BuildContext context) {
    return new Scaffold(
      appBar: new AppBar(
        title: new Text('TabView Test'),
        bottom: TabBar(
          controller: _tabController,
          tabs: _tabs
        ),
      ),
      body: TabBarView(
        controller: _tabController,
        children: <Widget>[
          Form(
            key: _form1State,
            child: TextFormField(),
          ),
          Form(
            key: _form2State,
            child: TextFormField(),
          ),
          Center(
            child: Text('Tab3'),
          )
        ],
      ),
    );
  }
}